New boiler or new hot water tank?

[zaffa]

We have an old Potterton boiler, I was once told on here that they are very good and reliable. It's an old system with a hot water tank and a header tank in the loft.
The hot water tank is small though and now that we have a baby and DSS here we've noticed that there are a lot of occasions where it doesn't refill enough between baths and so someone ends up with a tepid bath. Made worse by our electric shower just giving up the ghost ...
We've been looking at the new green scheme from the government and thinking seriously about getting a combi boiler and taking out the tanks - which would give us more space in the bathroom when we come to redo it eventually, but we don't want to take out a boiler that really is that good and replace it with a modern one which (from experience of everything I have ever replaced it seems) may be not as well made.
The other option I suppose is to replace the hot water tank with a larger one but it could only really be longer not wider due to the space constraints.
The heating is also a bit rubbish, radiators never seem to get hot enough all over and seem luke warm most of the time. Is that likely to be the boiler or do we need to replace the actual radiators themselves - or will some sort of chemical blast through them clear them out? Bleeding did not help.
Thanks for any advice!

I love @PigletJohn advice and is similar to what we experienced when we bought our house with old tanks and also a Potterton boiler. The boiler was fine until British Gas put in descaler which shifted so many lumps of scale it wrecked the boiler. They rebuilt it and just about the only thing left of the original was the casing!! They refuse to put descaler in the systems now.

What DH found was that when we redecorated each room, he lifted off each radiator (which weighed a ton as they were old) and flushed them out. It was apparent the system had never had inhibitor in as there was so much sludge in the radiator it was a miracle it ever got hot. I wonder if it is worth doing it with one radiator to get a feel for how much sludge there is in the system. Depending on the number of rads, lifting them off and flushing them is about a days job if you feel comfortable doing it?

What we did was when repainting a room, and changing the carpet we replaced the radiators. We got much smaller and lighter ones as modern rads are so much more effective. DH taught himself plumbing and using plastic piping it was a doddle. Depending on what you plan to do with your house and how old it is it might be worth considering?

When we needed to move the boiler though we bit the bullet. Replaced the old Potterton, got rid of the heating header tank and made it a sealed pressurised system. New hot water cylinder. What an amazing difference it made

@PigletJohn gives fantastic advice - and is likely going to save us a load too! Thank you! I think we will try our hand at the DIY clean - we've had one done by a plumber before and it cost a fair bit so handy to save that if we can. Your detailed instructions will be very helpful.
@MarieG10 I've spent today having a real inspection of the radiators and they all seem in fairly good condition and actually are heating pretty evenly and well. I need to get a better look at the three in the extension rooms as I suspect that may be what slows down the heat downstairs. I like your idea of inspecting them one by one and replacing as necessary - I'm wondering if it's the pipe work where the newer ones were added on that's causing a problem too (the various extensions / conversions on the house were done in a haphazard / DIY way so i wouldn't be surprised if it's something like that. Especially the utility room that is really nothing more than a lean to single skin plastic box with no insulation (but a solid roof and only an internal door from the house to it, allowing much heat to escape!)
Thank you to everyone that has commented and helped - luckily I was pregnant last year and so hot all the time so I didn't notice how cold it was until January where I just lived in the one room and was sleep deprived enough not to really understand what was happening. Normally I feel the cold terribly so I'm keen to ensure that the house is warm and I can have a long hot bath whenever I want one this year.
You've all been very kind to take so much time, and also save us a load of money by not ripping out the boiler when it will keep going (for now at least) gin and cake for everyone

the radiators in the extension rooms may need balancing with the rest of the house.

When we revamped our plumbing we went for a mains pressure system
we have a solar thermal panel that provides all of our hot water for 6 months a year and tops up in winter
then a 240 litre cylinder in the airing cupboard
and a vaillant boiler

mixer taps are easy as everything is at the same pressure
and there is no water in the roof

it is 12 years old now and still works brilliantly
(4 showers in a row out of the tank today)

yes, an unvented cylinder can give the best HW.

You do need a good incoming flow, and adequate pipe sizes within the house. Older houses often need to run a new supply pipe out to the pavement. Sometimes this is fairly easy.

I actually think that if we sort out the tank in the loft the problem will be resolved - because the tank up there is refilling at a small trickle which must be why the cylinder isn't refilling. The actual water reheats fairly fast there just isn't anything to heat.
I will look into how to rebalance the extra radiators - is that something we can do or do we need a heating engineer?

I think in a few years we will redo the bathroom and hopefully address the cylinder issue then if it doesn't need addressing before. It's in the way in the bathroom and stopping a better layout but after having looked at the rest of the house there isn't really anywhere else I can put it. I don't know
the difference between the two systems you mention - is the unvented one without a tank
In the loft?

You can balance radiators yourself

www.mumsnet.com/Talk/property/a3728238-help-never-ending-condensation?msgid=91181704#91181704

An unvented cylinder runs at watermain pressure, there is no cold water tank.

I would discourage putting it in the loft. It has to be regularly inspected (e.g. during the annual boiler service) and occasionally maintained, and it has a sort of "overflow" in case the pressure goes too high, so should be where it can be seen and heard. Ladder access is unsuitable.

Modern well-insulated lofts are very prone to freezing, especially if you are away on holiday or something and not using the plumbing.

The cylinder is at its best when close to the commonest point of use, either the kitchen or a bathroom. Although there is not such a waiting period for the water to flow as is usual with most combi boilers. It can often go in a corner of the kitchen, in a full-height cabinet, as long as whatever is next to (freezer, for example) can be rolled out of the way for full access.

it should be close to a drain (for the overflow) and the route of the incoming water supply pipe.

They are heavy when full of water. Often 200-250kg.

My cylinder is in a cupboard in the bathroom (built specially for it)
directly below the solar panel
and with shelving above it to keep all of my towels warm :-)

Thank you @PigletJohn. We discounted the loft almost immediately on having a good look up there and truthfully I think we will most likely accept the rubbish bathroom layout and leave it where it is if it's size is actually suitable for our needs for now.
When we do redo the bathroom we will see if there are any clever ideas. It's probably wisest to focus on the actual problem for now (cold house and cylinder not refilling).

Really appreciate your advice and that link is great - I've saved a copy of the thread and will give that a go when it cools down a little (I chose the wrong day yesterday to run the CH S it turned out to be quite warm!)