Yay a shotgun thread! I love them so here's a list that may help you.
Cheap as chips shotguns:
ASG Franchi Tactical - £25 - 260 fps
http://shop.tenburyguns.com/index.php?route=product/product&path=51_10167&product_id=9049
Had one myself as a backup gun. Great for CQB but is a single shot rifle. Very cheap but the shells it uses are quite crap - worth replacing with the ASG 30 round shells.
Mossberg 590 (Full stock) - £37.99 - 270 fps
http://www.actionhobbies.co.uk/Mossberg-590-Full-Stock-Shotgun-BB-Gun_AZJSR.aspx#.U9KO9tm9LTo
Single shot again, but my mate swears by it. Includes two 180 round magazines so it's brilliant for a lightweight back up.
More pricey but vastly better shotguns:
ASG Franchi SAS12 Shorty - £49.99 - 275 fps
https://jdairsoft.net/secondary/shotgun/asg-franchi-sas12-shorty-3-shot
Basic trishot shotgun. Louder than single shot rifles but a lot of fun to use. I've owned several incarnations of this weapon.
Maruzen CA870 Sawn Off - £99.95 - 285 fps
http://www.zerooneairsoft.com/product_info.php?cPath=269&products_id=1851
Pretty much a CQB sniper. I have one and it's my first choice for most skirmishes. Single shot but it's light pump means you can put a lot of rounds on target quickly. Built like a tank as well.
These are all "budget shotguns" (i.e. under £100) but they're solid weapons as there are less mechanical parts to go wrong compared to gas shotguns. I didn't list the Double Eagle single shots since they can be very hit or miss weapons (even if they're cheap) but the ones listed I have owned, currently own or have used.
Considering your request for "dirt cheap" guns I didn't include the G&P m870 range or other higher end guns. They also tend to be in the low 400s with fps.
If you need a bit more help PM me.