Looking for a nice pen suggestion

As other people have mentioned, Japanese pens. I like the Uni-ball Jetstream because I'm left-handed and for most of my life writing with ink was smudge city. I cannot smudge the Jetstream even when I try. They're not particularly fancy looking or expensive (three for a tenner, I think?) but they write absolutely beautifully. I like the 1.0mm ones but my wife prefers a 0.7mm. They're cheap enough to get a couple of each though. Also there's lots of colours available - I currently have blue, black and pink. I've written with some eye-wateringly pricey pens and they're not even close to being as nice as a Jetstream. Although it's worth noting I cannot use fountain pens so cannot compare against those.

I also like a Tombow brush pen, because the brush is particularly soft so you can get a good stroke variability easily. Tombow's ink is absolutely wonderful both in how it flows and how it looks. Brush pens are a bit of an acquired taste but I like them, especially for notating drawings or writing titles or similar. Probably not so much for longer-form writing though, in no small part because of the aforementioned trips to Smudgeville...

Slightly OT but related - I adore writing on Mnemosyne paper, even with the nastiest of ballpoint pens. Their notebooks are pricey but absolutely worth it. Midori paper is almost as good and much more affordable. Again, they're Japanese. Something about Japan and stationary.

As you're in the UK, I'll point you at The Journal Shop who have a great selection of high quality pens, paper and so on - but they can get a bit expensive.

Get a fountain pen. I have a $20 one and with a bottle of ink it lasts forever. It's nicer to write with and the ink is also darker and not as oily as ballpoint pens.

If you want ballpoint or gel pens, anything by Muji is also very nice. They sell a 6 pack of capped gel pens for $8, each pen has a lot of ink, and it flows very well. Be aware that because the company is from Japan, their pens tend to be much finer than western pens due to Japanese's compact writing.

For an entry-level fountain pen, I like the Lamy Safari.

I'd like to recommend any Caran d'Ache 849 ballpoint pen.

Swiss made, come in a variety of colours/designs, have a really nice shape to hold and a little bit of weight to them.

Roughly £15-£20 for the standard ones. Fancy enough to feel a bit classy and look after it, not so expensive that you'll have a panic attack if you lose it. I have a fluorescent orange one which makes it super easy to keep track of (pen thieves!) or to find rolling around the bottom of a black bag.

I highly recommend the Parker Urban Chrome. Used it for a good few years now, really comfortable to hold with a good weight, plus it’s within your budget and the metal design and finish is really nice.

I've been using Uni-Ball Eye pens for a while – they're pretty nice, although the ink does take a few seconds to dry, and they stop working quite so well when they start to run out.

I'm sure this will go against the topic and the suggestions already, but if you're like me and lose a lot of pens, then getting an expensive pen isn't as appealing. I have had nice pens in the past that I have lost for various reasons, although I think if I had a fountain pen with an ink well I would find that a bit harder to lose.

What I normally do is buy a bunch of misprinted pens on eBay or Amazon. They're normally quality pens. A lot of them won't write, but considering how many nice pens you get for the price it's normally acceptable. They'll be plastic, but personally I don't like metal pens. I have a few nice metal pens and I stopped using them because I didn't like the way that hey felt on my hand.