The short answer is No. The vast majority are illegal, but there is an alternative classification. What is this is this? Your EPAC may qualify to be re-classified as a “Low Powered Moped”. You can purchase one from Wisper.
When the bike is certified, the details including frame number are held by DVLA so the police can always check that you bike has a legal Full Throttle.
Since 2016 it has been illegal for standard legal EPACs (Electric Pedal Assist Cycles) to have Twist & Go throttles up to 15mph. You can have throttle that works up to 4mph without pedalling and this throttle can continue to work up to 15mph as long as the pedals are being turned. The vast majority of legal electric bikes with throttle conform to this standard, but many may exclude the pedalling to 15mph facility.
The standards were defined by the EU and incorporated in the UK Electrically Assisted Pedal Cycle Regulations 1983 (SI 1983 No. 1168) as amended by SI 2015 No. 24. The amendment was passed at that time to harmonise with EU Law.
The next defined vehicle above EPAC is “Low Powered Moped” (L1-e). This vehicle has the same restrictions as an EPAC. 250watt nominal motor and maximum of 15mph under power, but stipulates several other requirements including mudguards, lights back and front operated by 1 switch, side stand, and brake levers with ball ends. Any EPAC with this specification can be certified as a L1-e, “Low Powered Moped” and legally use a Twist & Go or Full throttle up to 15mph.
No electric bikes are classified to be sold as L1-e bikes and each bike has to be tested and Certificated by DVSA. You can find the Test Centre nearest to you and make a booking at: https://www.gov.uk/government/publications/specialist-schemes-testing-station-map/individual-vehicle-approval-iva-test-centre-locations
When your EPAC has passed the test, you will be issued with the Certificate that must stay with the bike. It is valid for the life of the bike. The bike manufacturer should be able to advise you how to de-restrict the throttle up to 15mph.
Alternatively, you can purchase a new Wisper electric bike complete with the Certificate and derestricted throttle. Wisper will keep a copy as a record for the Authorities.