At the moment a DIY ebike is perfectly legal in the UK, as long as it doesn't exceed the performance and power limits. It can even have a throttle, as the funny sort of hybrid law we have at the moment means that there is no need to have EU Type Approval for an ebike that's ridden in the UK, all that's needed is compliance with the regulations.
This will change when the government get around to removing the UK-only EAPC regulations from the Statute Book and fully accepting the EU EPAC regulations as the only type of legal ebikes allowed. From that point on, any new ebike would have to be EU Type Approved and carry a sticker saying it had been tested and was compliant with the regulations, which would outlaw all DIY ebikes. Like all laws of this kind, it couldn't be applied retrospectively to older ebikes though, and there is likely to be a major problem in determining the age of any bike; "was it converted to an ebike before or after the adoption of the EPAC regulations?". The government is showing no sign of wanting to tidy up the ebike laws, though, so we are at present stuck with the rather messy system that allows both types of ebike to be sold and used perfectly legally, something that works to our advantage as we can cherry pick the regs we want to comply with
Getting a more powerful ebike registered isn't that easy, but can be done. It's pointless to try and register one as a "low powered moped", as the speed restriction is exactly the same as for an ebike. You could register a high powered ebike as a motorcycle, using the MSVA test and approval route, but it would then need an MOT certificate, insurance, tax disc, number plates etc. At least one chap has registered one of the stinky two stroke bicycle conversions using the MSVA route : http://www.users.globalnet.co.uk/~pattle/nacc/arc0497.htm so you could do exactly the same with an electric bike, with the added bonus of being road tax exempt (although, just like my exempt car, you still need to get a free tax disc every year and display it).