Hosting advice

[#1]

Can anyone recommend a cheap and ideally UK-based host for a personal website, which currently comprises four Wordpress blogs[1], assorted vanilla HTML pages and a few hundred images? I get the impression that Plus's offerings are not seen as the best option? I'm willing to pay for something that works, but it is just for a personal site so not worth spending much money on. No e-commerce or secure transactions etc would be required.
I've been with Plus for many years (inertia and no serious problems), and as a result currently have various pages and files strewn across an assortment of plus.com, ccgi and "free trial" PAYH locations, and elsewhere. The PAYH site just got suspended for exceeding its traffic for the month (it seems to be doing about 3GB/month), and this seems like a good time to have a rethink and get everything in one place.
I'm not expecting to ever get major traffic (my writings on railways are never going to be the new Facebook), but I have been "slashdotted" a couple of times in the past; I don't care if the website gets suspended for a few hours when that happens, but I'd want it to come back again and I don't really want a bill. 
[1] There is probably a better solution than separate Wordpress installations for mydomain.co.uk/fooblog,  mydomain.co.uk/barblog etc for my four subject areas, but it works reasonably OK for now.

[#2]

I don't know exactly what your budget is but if you have a small bit of hosting stills of your own you may be best going with a VPS. It would provide you with a huge amount of flexibility, you would never look back.
I moved from Plus Net's servers many years ago for similar reasons. I went to Eukhost and got a VPS. After installing Virtualmin you have a fully ready hosting server all of your own. Virtuilmin is free and really simple to install and use.
My Eukhost VPS costs about £20/month but you can get insanely cheap ones with ThrustVPS for around £5/month although I have only ever used these for short periods so I cannot verify how good they are.
My VPS with Eukhost has been rock solid for at least 5 years, I have PRTG monitoring it so I would know if there was any major outage.

[#3]

Thanks, I'll take a look at them. My budget is "as low as sensible without getting something frustratingly rubbish", really.
I've found places hovering around 1 to 3 quid a month, but have a gut feeling that the cheapest end might not work well, while with some I might be paying for their advertising budget rather than their technology(?).

[#4]

If you don't need your own server, VPS, etc., - and I can't really see that you do, I'd suggest looking at the hosting pages on visn.co.uk (Cheshire). I'm not suggesting using them but they do show standard charges for such things, various options, with no funny business. It'll give you an idea.
(The prices quoted are per year, not month, btw!)
Having 4 SQL databases to run 4 lots of Wordpress (if I understand you right) might make things more expensive.
Work out with someone how much bandwidth you are actually likely to use, that could make quite a saving, too.

[#5]

As long as different table prefixes are used for the separate WordPress installations then only one MySQL database is needed. Specifying the table prefix to be used is part of the standard WordPress set-up process.