All the ones I listed fit in that sized boot without the wheels coming off, and I think all of them except for the Mutsy are under £500 (we only got it because we found it second hand). This is our boot, it's absolutely miniscule!! NB DS2 does travel in a proper car seat I promise :o
Eezy S+ is newer - I hadn't seen that :)
Worth noting - all the buggies recommended take a Maxi Cosi car seat. When we went to look at the Cybex Balios S, which was my favourite, the sales assistant explained that the Cybex and Maxi Cosi car seat adapters are identical, and in fact even though it's a Cybex buggy with a Cybex car seat, we'd have to order the Maxi Cosi adapters!
I later found out that those same adapters have been used by a lot of car seat manufacturers so actually you can put any of the following company's seats onto Maxi Cosi adapters:
Maxi Cosi
Cybex
Joie (except Juva)
Besafe
Nuna
And with an interim adapter between the maxicosi adapter and the car seat:
Recaro
Axkid
Then a couple of one offs - the company's other seats don't fit but this specific one does:
Cosatto Dock
Venicci Ultralite
And then, if your pushchair model is popular in the US (e.g. Babyzen) you can usually get Britax Click & Go adapters for it instead if you prefer - those fit the UK Britax seats.
You do have a huge choice in compatible car seats, which isn't always immediately apparent. Since you said you're on a tight budget and car seats (especially with a base if you want one) can be pricey these are the cheapest ones from that list in case you don't find a good deal with the car seat included which works out cheaper:
Without base
Joie Gemm £70
Maxi Cosi Citi £80
Joie i-Snug £90 *
Maxi Cosi Cabriofix £100
Britax Babysafe £100
Cybex Aton £100
Maxi Cosi Tinca £110 *
Cybex Aton 5 £120 *
Besafe izi Go £130 *
Venicci Ultralite £130 *
Joie i-Gemm £130 *
With base
Joie Gemm £160
Britax Babysafe £180
Maxi Cosi Cabriofix £195
Joie i-Level £200 *
Cybex Aton 5 £220 *
Britax Babysafe i-Size *
Maxi Cosi Tinca £245 *
Nuna Pipa Lite LX £250 *
The ones with stars by them I'd say are not "budget" ie bare bones car seats - they all offer something a bit extra. The Tinca/i-Snug are budget models technically, but they're absolutely brand new to market so I've included them as they have some of the features which would have been exclusive to "premium" models in years gone by.