Not quite a solid carrycot, but have you looked at the M&P Pliko/Pliko Switch? Coverts from pushchair to lay flat pram very easily, and folds up umbrella style.

the loola can come with a carrycot, you can get them on ebay, again it folds up easily etc and even without the carrycot the seat lies flat, you can also a attach a carseat to it. i think the new one is called the loola up? we have an older model.

i really love my out n about nipper 360 no carrycot (tho i am not usre inewer models do?) but it goes totally flat and then i just used a cocoon thing like the phil and teds cocoon to make it snug and cosy and i coudl pick little one up in that and lift them inside without disturbing them its about £180 nad great, leightweight a breeze to push etc, i use it for my 14mth old and occasionally my nearly 4 yr old if he is poorly etc i can stick dd in a sling/back carry and then put him in the puschair for the school run.

I got my hauck condor for ?249. Came as travel system with carry cot.
Its really sturdy, folds easily(into my mums tiny micra) and is nicely padded for dd. Reclines fully too

Another recommendation for the Loola here. I have two of the old style Loolas, and my sister has the Loola Up. They're readily available on eBay, as are the hard shell carrycots (the Windoo). The Windoo can also be used as a lie-flat car seat

The Loola can also be used parent facing as well as forward facing once you're using the pushchair (which is suitable from birth if you don't want to buy the carrycot).

The folded Loola (without carrycot) also stands on it's end very neatly, making it ideal for a small hall. It can fold with the seat unit attached (whether the seat is forward facing or parent facing!).

I should get a job selling Loolas!

Have you thought about a Baby Jogger City Mini. They are slightly more expensive than other buggies, but they are fantastic - amazing fold, relatively light, big basket, huge seats so your child won't outgrow them.

They are not the cheapest - it will set you back about £200.

As for the carrycot, they have a compact carrycot (approx £100) and a deluxe hard carrycot (approx £150).

The new 2012 models are just entering the shops so you'll probably be able to grab a 2010 or 2011 model on sale somewhere.

Lots of mums on here love their baby joggers!

If you buy the right pushchair then you shouldn't need a stroller ;)
I would have a look at the Babystyle Oyster, Bugaboo Bee (no carrycot), iCandy Cherry or Peach (if considering second hand), or Baby Jogger City Mini 4. One of the Maclarens takes a carrycot too. There's also the Petit Star Zia and Quinny Zapp Xtra which are both small with newborn options.