On Thursday (now Sunday) I went to my dentist expecting a filling, after examining me I was told my wisdom tooth was broken and needed to be removed. After having an X-ray my dentist thought he'd be able to do it himself rather than referring me to a specialist at the hospital.
He gave me a filling on the tooth next to my wisdom tooth, and then fairly easily removed my tooth. He did think that possibly the very top of the root hadn't come out but if that was the case shouldn't cause a problem. It bled for most of Thursday but was pleased that on Friday morning the clot had formed. On Saturday morning the was still there however during the day, an ache like pain started and the whole of my face was now aching. Saturday evening I had a look and the clot was gone, and now all I can see is a grey/white something, where the tooth and clot previously were.
Chewing on the other side is hurting my jaw. Typically this happens on a bank holiday weekend, so I rang 111 as instructed on dentist number, as thought may be dry socket, however was offered appointment on Tuesday. NHS website says see dentist immediately, so did think it was a contradiction by them when they can't do anything at all for me. The pain isn't horrific, and I am a wimp, however I don't want it to get horrific.
I am a smoker but have not smoked since tooth was removed. I haven't poked or touched it at all, and have rinsed with salt water when told I should.
Please can somebody advise me on what to do about getting to a dentist sooner, and any home remedies I can try to limit any possible problems!
Thank you in advance!!

I'd call another dentist, if possible. Dry socket is painful.

Thursday to Sunday is nothing. If you aren't in intense pain, and if you do have painkillers to take, take them. I've had extraction pain for as long as 3 weeks, with half of that being flat out on Vicodin.
You shouldn't be chewing. Eat yogurt and other soft foods.
The whitish thing is normal.

I have literally called loads of dentists but due to it not only being a Sunday, but a bank holiday weekend, every recorded message informs me to call NHS 111 to get emergency treatment. Turns out there's no such thing in the uk!

Of you came here for advice then read it. The clot has gone because it did its job. The blood clot healed the extraction site and now you see the outcome, the white which is new skin forming. Only soft foods, no chewing.

Lovely, that's what I was after! Sorry if I've annoyed you by asking a question though!

One last thing, is it normal to have a pretty nasty taste in my mouth?

Yes. That is normal, the nasty taste. It is the blood that has mixed with saliva and the medication from the freezing.

You can use a mouthwash, just don't sluice it around your mouth, and you still have to brush your other teeth so toothpaste will help too.

Awesome. Thanks for your help