A 1960's house with UFH probably has an uninsulated concrete floor. Short of digging it up, you will not be able to put wet UFH in. The old heating cables might still be in good condition, but will be expensive to run unless you have an Economy 7 type electricity tariff, or plenty of PV solar panels.
If the floors need to come up because of, for example, heave, cracks or slag content, you may as well insulate and add wet UFH while doing it. Otherwise it will be uneconomic.
It will have cavity walls, which should be insulated unless there is some severe problem with the walls of your house preventing it.
Loft insulation should now be ten inches deep.
If it has wooden windows they are probably rotten.
It might need a new roof.
I strongly recommend running a new plastic incoming water supply pipe all the way to the pavement stopcock or water meter (you will probably have to pay the water co an exhorbitant amount to connect it unless there is lead piping and they replace theirs at the same time you replace yours, or you change from unmetered to metered, and have your trench ready dug and your new pipe ready to connect when they dig the hole.
A 25mm plastic pipe will usually give good flow, but 32mm pipe is even better, costs not much more, and is the same amount of work to lay.
With a big water pipe you can have a pressurised water cylinder such as a Megaflo, which I would usually recommend over a combi, unless you have a small home with only one person wanting to turn on a hot tap at any time. Get a System Boiler which also has less to go wrong than a combi. You will not need any pipes or tanks in the loft.
The electrical cables with probably be PVC and still safe, but the lighting circuits will probably have no earth, all the accessories will be out of date and possibly worn out, and there will be far too few socket outlets, so you may as well have a complete new installation. Rewiring a house costs the same as buying a second hand car. Ask the installer to quote for RCBOs (he will know what that means unless he is very ignorant) and dedicated circuits for the kitchen and the utility room.