Hiya,
Do you have any contract with your flat mates? They should give you a months notice, but you may have to check on that if you've not signed a contract with them. You say you're starting to feel ready to move out, was this the case before you heard that you're flat mate was going to ask you to? If so, then one way to approach it may be, not to even ask them about what they have been saying, but just say that you're thinking about moving out, and if you can arrange a date that suites you both? It may give them a chance to say 'I was going to ask you if you'd be happy to move out because...' Just make sure that you're not only moving out because you feel forced to.
Moving can be daunting. I find
www.rightmove.co.uk a real help. You type in your postcode, and enter how much you can afford etc, and it'll give you a list of all the properties that are available in your area. When you find ones you like, contact the letting agency and arrange a viewing. If you like it, then the letting agency can explain the rest of the process to you.
In terms of a guarantor I'm not sure... I didn't need one, they just needed the details of my employer and a reference from them. My boyfriend had to have one, but he was able to post all the paperwork to his dad, again I think it depends on the letting agent. I wouldn't worry too much about this, as there are ways and means to get around it. The best thing to do is focus on telling your flat mate and trying to find a place to move to. The rest the letting agent will help with.
I moved about a month ago, so if there's anything else I can do at all just message me.
Hope it all goes well, it's a massive step, you should be really proud of yourself xx