There are new cheap folding bikes for sale on the Argos web site. At the time of writing there is the Raleigh Active Fold-A which is a 7 speed, 20″ folding bike with an alloy frame and stem. It has Shimano gears and shifters, alloy rims, adjustable handlebars and a quick release seat. It weighs in at 16kg and costs less than £200. There is even the single speed version of this bike, the Active Fold S which is about £50 cheaper.
Argos also have the 18 speed Challenge 26 inch Mountain Bike, this is a unisex bike with a folding frame. This weighs 17kg and the fold doesn’t get any smaller than the 26 inch wheels do, but it is less than £200. Wheel size is of course one of the main factors in the folded size of a bike, which is why the Brompton folding bikes always win with their 18 inch wheels.
Halfords have their own Apollo folding bikes that have 20 inch wheels and a lightweight aluminium frame. The flagship model is the Apollo Transition Folding Bike which has 6 speed Shimano revo-shift gears, alloy V-brakes and weighs only 13.1kg. The Apollo transition is around £250 whilst the cheaper Apollo folding bike is about £100 cheaper, but has a steel frame, steel brakes and is just single speed.
Evans Cycles stock a range of quality folding bikes including Brompton, Dahon and Montague and there cheapest are usually the Tern Link C7 bikes that can be picked up for about £300
There are quite a few sellers on Ebay selling new folding bikes as well as reconditioned folding bikes so that might be a good place to look too. There are also some sellers who specialize in putting together Bromptons, presumably from parts they have acquired along the way. This is of course perfectly acceptable as the Brompton range is totally modular with most parts being totally interchangeable between different bikes.
The real Ebay bargains are made by spotting something where the Ebay ad hasn’t been put together particularly well. For example my bike is a Brompton M6R but the title of the ad was ‘Brompton 6 Gear Folding Bicycle’. I wouldn’t have found it if had been looking for ‘Brompton Bike’ or ‘Brompton M6R’, but instead I had an ebay search for ‘Brompton 6’ saved which is how I found it and how I was able to get a bargain.