It's professional and reasonable to tell a company that you are interviewing with that you have already received an offer from someone else and are considering it. if they say, "Oh, well nevermind," then they weren't all that interested in you, and that's fine. But there's a decent chance that they'll say, "Huh... well, that company usually knows their stuff. If they're willing to hire this person, we probably would be, too. Let's put together an offer and try to do better than them."
There's a whole awesome guide on salary negotiations out there that makes it a little bit less scary. It includes stuff like "how to say that you've got another offer." One of the suggestions from that article is to say something like,
“Yeah, [COMPANY_NAME] sounds great! I really thought this was a good fit, and I’m glad that you guys agree. Right now I’m talking with a few other companies so I can’t speak to the specific details of the offer until I’m done with the process and get closer to making a decision. But I’m sure we’ll be able to find a package that we’re both happy with, because I really would love to be a part of the team.”
When negotiating for starting. Keep in mind-- these companies interviewed you as one of several candidates for the position. It would be unreasonable of them to assume that you haven't interviewed several other companies to see if you'd be a good fit for them, too.
It also mentions how to extend your timelines and such. You can say something along the lines of
“I’ll look over some of these details and discuss it with my [FAMILY / CLOSE_FRIENDS / SIGNIFICANT_OTHER]. I’ll reach out to you if I have any questions. Thanks so much for sharing the good news with me, and I’ll be in touch!”
when you need to just end a high-pressure conversation. The nice thing about that tactic is that it puts the onus of the decision on someone besides you. If you said, "I need to think it over," They can just say, "No, you need to reply right the hell now." If you say, "I need to discuss this with my significant other" (they don't have to know if you're single, how the heck would they know?) then they can't really hit back. it's a person who isn't in the room/isn't available right now. The decision-making power is out of the room; they just have to wait until you get back to them.
Different companies can/will reply in different ways when you say you need a little bit more time to consider their offer and others. Some will say, "You have two days" or something like that. You can push back and say, "I'm afraid that won't be enough time, I'll need at least X days." Depending on the company, that might work. If it's Jim's no-name-company, you might be able to get away with it. if Jim's no-name-company wants to rescind your offer, that's a fairly out-of-industry-standard practice that lets you know you've probably dodged a bullet. (It could be that Jim's no-name-company desperately needs a guy in the office ASA-freaking-P, but that also could indicate a disorganized and difficult work environment where you'll need to wear about 50 different hats at once). If it's a huge-name company, they probably won't give you more time, because why should they? A Google or a Facebook will just say, "Cool. We've got other candidates who are just as good as you and who won't ask for more time. We'll just take one of them." if you try to push back too hard. Generally, they're not going to just insta-burn the bridge (IE if they say "You have 48 hours" and you say "Could I maybe have 60 hours?" they aren't going to tell you that you no longer have an offer). They'll give you a timeline, you'll counter that timeline, they'll counter back, you'll settle on something most likely. But bigger name companies can afford to play hardball and will play hardball to try to prevent you from going somewhere that would force them to pay you more if they wanted to hire you.
Now, as to your last question:
what happens if I sign a contract and then effectively quit (in favour of another offer), before even starting? Does the probation period notice even apply?
I can't speak to the UK's laws on the matter, but it's absolutely unprofessional, and it would be a black mark in your file if you ever wanted to work with that company in the future. Per some googling you'd probably be okay legally if you quit before signing a formal acceptance letter. Otherwise, it would depend on the terms of your employment contract; you may be required to pay back signing bonuses or pay an early termination fee depending on the contract.
The good news, should you need to quit after already signing on and really upsetting the company, is that in today's litiguous world, most companies prefer to simply verify employment when contacted about a former employee and to leave it at that, regardless of how great or how terrible a particular ex-employee was. Most likely, you'd be blacklisted for the company you burned, but they wouldn't really spread anything to other companies. That isn't to say it's impossible-- if the HR person who handled your file moved to a new company that you applied for later, they could recognize your name and just deny you an interview without you ever realizing it. It's unlikely, but it's a possibility.
My personal opinion is that you should be honest with employers the whole way through, set your own deadlines for when you'd need to hear back from everyone, communicate offers and deadlines, and then accept an offer that you intend to stick with. Unless the company is actively horrible enough that you hate it and need to get away, I would stick with whoever's offer you accepted. Keeping your word is important, and it isn't as if you can't hop to a new job in 9 months to a year when you're in the software industry.