It is not claiming authority, it has authority because the UK government agreed to this. The UK does influence EU regulations, that is the idea: have the same regulations so you can have one domestic market with the same regulations, trade without friction.
At the end of the day the EU is the supreme authority over the UK regulation and judicial process there's no arguing that, and 27 other nations have an input into UK regulations. If the UK does not like a set of regulations it has to form a big enough minority with other like minded nations to stop or veto such regulations.
Yes the other 27 nations have a say in creating EU law that then becomes UK law. BUT, and this is a very big but, we have a say in these laws, we have a veto. I can tell you from first hand experience, who do you think was the driving power behind CE marks, EMC standards? When I say driving, I mean had the majority of the expertise so when EU laws were created they were based on data, and imformation from...you guessed it the UK. So UK standards effectively became EU standards. So you see it works the other way as well, that's what a partnership is.
You state you want the UK to make it's own laws, well it does, but it also helps create EU laws. Laws that are created by the EU are generally world leaders in terms of requirements. Why should UK citizens have to expect lower qualities of produce, lower protections in order to have trade deals which already exist by being part of the EU?
What regulations do you hate so much, that you want out? Working Time directive? CE? Environmental? Hoovers (UK pushed this) ?
How about someone stopping the Conservative parties regulations like the bedroom tax, massive reduction in police / teachers / NHS funding and all the problems is has created - London centric spending, Russian money, Saudi money, massive cost of houses, lack of housing, windrush, massive income equality, homelessness? How about fixing the problems that actually affect everyone day to day, those that are directly the responsbility of Govenment? How with all of these problems can you trust them for one second to negotiate all the trade deals needed with a WTO no deal Brexit? I say this Govenment because JC is just as useless and isn't remotely close to winning an election.
The UK is broken, and massively devided. Leaving the EU will not fix this.