I picked up a Britax buggy at a car boot sale for a mere £5 and it's great.  It's a travel system type thing - not sure if it has a name, it's about 9 years old.   It's so strong, but it is also quite big (even when folded), so there are pros and cons.   Below is a wire tray and it will support support a 3-year old laying down on it (tested when we went for a very long walk).     So it can be worth looking around car boot sales at the older style buggies, as they can be stronger than the new ones.

I have just been on holiday with my lumping great heavy toddlers and took my Petit Star Global pushchair with me (similiar in style to M&P Pliko which I also recommend)  - My eldest weighs 19kg and is enormous and he slept and was pushed around in it no problem.

His 23 month old brother is the usual passenger in it and it's plenty roomy enough for him and puts up with a lot of bouncing around and tantrums! 

I am currently selling mine as I don't need it any longer - it's in the 2nd Hand Section on the site if you are interested.

 Best of Luck with finding something suitable - I would recommend scouting around mothercare and John Lewis to find one you like - then hunt for it on eBay or kiddicare.com !