Can you look for a job in the UK without a visa?

It is absolutely legal to look for work on a UK business visa (meaning a standard visitor visa). You do not need a work permit. However there are some serious traps that you can fall into.

• If you have a pre-arranged interview, you will be fine (as long as the job is real and one for which you could reasonably expect to be given a work permit.) If you need to come to the UK for an interview, apply for a standard visitor visa.
• It must be realistic and necessary that you have to come to the UK to look for work. Frankly that is extremely unlikely to be true for the pre-interview stage. Every job above retail server allows - no, requires - that you apply online. You will never get a work visa for a low level job, so there is no point in applying for them. For every other job you gain no benefit from being in the country, so why would you spend money to come to the UK? Immigration will assume that you have another agenda, and you will probably be denied a visa.
• If you say you are coming as a tourist, but they find evidence that you are coming as a job hunter you will be banned for deception. It doesn't matter that looking for work is legal on the visa you have - you lied about your purpose. Now if you are genuinely on holiday and genuinely coincidentally run into someone who offers you a job, that will probably be OK, but any pre-planning will get you in trouble.

I don't think there is anything legally preventing you from doing so.

However, see it from the perspective of an immigration officer. How can they be sure that once you've found a job you won't start working right away?

Then you have the fact that if the job can wait a little while for you to start (usually more qualified jobs, where prospective employers are willing to wait for you to end your notice period with your previous employer, deal with visa issues, and usually with slightly longer processes, multiple phone and face-to-face interviews...), then there's no reason for you to arrive in the UK first and look for jobs while there: you can do all the initial preparation (apply, go through phone interviews...) while outside of the UK, then plan face-to-face interviews and get to the UK for those.

On the other hand, jobs where you could find an opening quickly via a more direct door-to-door type approach are usually lower paid jobs, where you are expected to start quickly, definitely not with enough time to get back home, apply for a work visa, get one, move, etc.

In regular times, the chances of you slipping through the net would be quite large. Only if something tips them off and they start digging would there be an issue. But in this period where travel is often restricted, IOs will naturally be a little more inquisitive of the reasons you are coming to the UK, and once you say "I'm looking for work", they won't hear the "but I won't be working on this visit, just looking for a job".

If you've watched any of the "Border protection" shows, you must have seen that finding a pile of resumes in your bag, or a suit and tie when you pretend you're on holiday, usually ends up badly.

Don't forget the UK are flexing their muscles to try show that they are left with a shred of power after Brexit. You don't want to get caught up in that. Not only is it highly inconvenient and uncomfortable on the spot, but it will in addition leave a stain on your record, so be extremely careful.