Asda and Boots hung on longer with in-store store processing labs, but these have gradually shut down leaving your choices for getting film processed somewhat narrower. Unless you are very lucky and have a local lab then you will need to get your film processed by mail order.
At time of writing (November 2016) these are some of the companies doing 35mm film processing by mail order at the budget end of the market in the UK. The prices are for developing and scanning either to CD or for download with the negatives posted back to you. They will all provide a set of 6x4 prints for around £6.
The size of scans varies. I have tried to find the prices for medium sized scans that could be used to make digital prints to 6x4. You still have the negatives for conventional printing of enlargements. Most return the scans on a CD. Some upload them to a transfer site which means you can download them before the negatives reach you in the post. This could reduce the effective turnaround time by two days.
Develop and medium scan £5
Develop, medium scan (2988x1722), scans uploaded to We Transfer, negatives by post, £6
Need special mailers, available on request from this web page
They closed a lot of shops after being bought by Timpson in 2008. Some branches of Timpson will take a film in for processing and send it to their central lab with around seven days turnaround. They also offer a mail order service. Scans are thought to be quite low resolution, but you do get a set of prints.
Develop, print, scan to CD £8.50
Develop, medium scan to CD, £9
DS Colour Labs
Develop, Medium scan to CD, £10
Develop and Scan, to Dropbox, negatives by post, £11
Black and WhiteIf you shoot black and white you have a few budget options too. It may be cheaper to get prints rather than scans.
Develop and medium scan £8.99
DS Color Labs
Develop and medium scan to CD £14
(compared to Develop and print to 6x4 £10)
Develop and high res scan to CD £18.75
Higher Quality OptionsIf you are looking for higher quality, professional standard, processing then I would recommend Peak Imaging (who I have used for 35mm and 120 films). The Darkroom UK also has a very good reputation, although I have not used them, as does Karen Willson.
The Darkroom UK
Develop and medium scan to cd £18
Develop and medium scan to cd £20.85
Develop and print to 6x4 £19.85