Web and weather cams are usually fixed cameras uploading an image every few minutes. They are often run privately and may not always be working. I have not found any cams in Bedford. The live cameras below are within 40 miles and usually have similar weather patterns

Clifton weather cam (10 miles south)

RSPB Sandy bird feeder (10 miles east)

Ampthill weather cam (12 miles south)

Stopsley, Luton (20 miles south)

Cambridge (30 miles east)

Winslow, Buckinghamshire (30 miles west)

Peterborough weather cam (40 miles north)