It might be quite hard to get something that will be good and last you for £200 particularly if including the car seat in that but even if not quite a challenge. Hmmmm.
Do you want a carrycot or a lie flat seat suitable from newborn to toddler? Do you want it to face you just for a young baby or the entire time? Quite important question - Are you likely to need to fold it for public transport whilst holding the baby?
You won't go wrong with a city mini as mentioned (they take car seat adaptors and a choice of carrycots). Probably can the get the buggy for circa £200 but not a carrycot too. The Britax B Agile is similar in function with some small differences. The handle for example is lower so tall people using it could have a problem. Probably you could bring this in under £200 if you bought a 2nd hand or on offer carrycot from ebay or similar. Just the buggy is well under £200 now. The Graco Evo is £279 from mothercare, reversible lie flat seat they often have 10% offer codes so that's quite close to your budget. The Jane Muum is £250, very light, does fold in one piece etc but you need both hands to fold it and I found it rather big. Jane Solo Reverse similar functions but slightly different style.
If it might be more your kind of thing several maclaren buggies go from birth and one has a soft cot attachment so a newborn can face you. For a parent facing option in this style the Njoy/Petite Star Bubble is due out soon and is suitable from newborn (I've seen one though and it does not lie totally flat).
To note there is relatively little choice of parent facing pushchairs in the this price range. Also parent facing ones often but not always fold in 2 pieces. If they fold in one (ie bugaboo bee) then they tend to be quite a bit more expensive.
What you want it to do is the most key thing, which of your requirements are most important. There's usually a compromise or two somewhere along the line 