1981 would be the 15th edition of the "regs." We're now on the 16th edition, but off the top of my head I can't think of any major changes that would affect this particular issue.
Although new washers now always come ready fitted with cord and a standard 13A plug, it's quite permissible to cut off the plug and hard-wire it. The wall outlet would normally have a double-pole switch so that the unit can be isolated easily.
As the regs. prohibit the installation of any "socket outlet" (i.e. receptacle) in a bathroom, except xfmr-isolated shaver types, a washer would have to be hard-wired. And although domestic dryers over 3kW are rare, the 4kW types have to be hard-wired even when fitted in a kitchen or utility room, as the loading exceeds 13A.
I think the space factor is probably the most restricting thing: Even without electrical considerations, most bathrooms here are just too small to fit a washer in. There's possibly a cultural thing as well -- "We've never done it that way before" kind of thing.
By the way, whatever the IEE would have you believe, it isn't actually mandatory to follow the regs. on domestic wiring. They're generally accepted and followed as good practice, but there's no legal obligation. Commercial is a different matter, as is Scotland.
Which part(s) of the U.K. did you visit? Quite a bit different to the States, isn't it?