Every employer I have ever had has had that clause and every one of them was fine with adding an exemption to the contract for my (registered) company as long as it doesn't compete with their business. This effectively gives me free reign to do whatever I want.

Almost no one reads / negotiates their employment contract in the UK, but businesses generally have no problem with it and an employment lawyer will cost £50-100 an hour to review and advise on the terms you've been proposed.

If you're already working there then you can get the company to agree to it in writing - ask for permission to do something benign, frame the request as doing outside work for your company, do what you like.