"There must be a way that they are getting inside, but you might need help from pest control to discover it and block it if the problem continues."

Not unless you make your house airtight, which might have more serious consequences.
The spiders are there because there's a food source, so if you remove the spiders you'll have insects to deal with, unless you want to take drastic action and have the place fumigated.

I agree that they're false wolf spiders - they apparently originate from Europe so are used to milder climates, hence wanting to come indoors (poor you!). They are rare in the UK, except in London. I regularly see them in our garden each year (we're near the Common too), spinning massive webs. There must be a way that they are getting inside, but you might need help from pest control to discover it and block it if the problem continues... good luck!
http://www.uksafari.com/false_wolf_spiders.htm

 That second picture really does not look like any British spider I have ever seen.  Perhaps try calling London Zoo and speak to an expert who will be able to identify it. Good luck

Theyre false wolf spiders. They can bite, but arent particularly harmful to humans.

https://en.m.wikipedia.org/wiki/Zoropsidae

Wowsers! Reminds me of living in Aus - they had massive spiders there called Huntsman Spiders - they ran like the wind and looked frightening but it’s the little ones over there that will kill you!

I have never seen anything this big but did a quick google for you and it looks as if our UK spiders can get this big. Do you think it’s any of these here? Let me know how you get on! And good luck!

http://home.bt.com/lifestyle/house-home/cleaning/10-common-spiders-youll-find-in-a-british-home-11364003665066

It’s difficult to tell how big they are but if they’re as big as they look in the photos I wonder if they’re escaped pets from a neighbour. A friend of mine had that happen to her! I don’t know how you’ve stayed calm, I would have moved and got pest control in I think!

We live on a road just off Clapham Common and the past few months we have found two rather sizeable spiders in our bedroom - these do not look like normal house spiders (good job we aren't that screamish otherwise I think the house would have been bulldozed by now!)

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1. Does anyone know what these spiders are?
2. Has anyone else come across these in the last 6 months or so?
3. Any suggestions on what we should do as worried there are many more now! 

Thanks!