Once upon a time yes, but the modern Intel graphics are great. Probably not as good as AMD or Nvidia cards but integrated graphics cards will manage most but the most modern or graphically intensive games.

Edit: A lot of turn based RPGs are probably going to be fine, that's a lot of what I play and I've not found any that are trouble.

Some laptops i found quickly on Amazon UK. If you have other websites for UK we can take a look.

https://www.amazon.co.uk/Lenovo-V110-15ISK-80TL0010UK-Processor-Resolution/dp/B01LXDF5S3/ - £400

Lenovo V110-15ISK (80TL0010UK) 15.6" Laptop Intel Core i5-6200U 2.3 GHz / 2.8 GHz Turbo Processor, 4GB RAM, 128GB SSD, 1366 x 768 Screen Resolution, DVDRW, HDMI, USB 3.0, Bluetooth 4.0, Windows 10


https://www.amazon.co.uk/Dell-Inspiron-Laptop-Pentium-Windows/dp/B01N9OJEE3/ - £419

Dell Inspiron 15 3000 15.6" Laptop (Intel Core i3, 8GB RAM, 1TB HDD, Windows 10) - 2017, Matte Black


https://www.amazon.co.uk/dp/B01MT119HM/ - £453.94

HP 15-ay110na Laptop (15.6 inch, Intel Core i5-7200U, 8 GB RAM, 1 TB HDD, Windows 10) - Turbo Silver


https://www.amazon.co.uk/ASUS-VivoBook-X556UA-DM898T-Notebook-Processor/dp/B01MY76TRY/ - £469.99

ASUS VivoBook X556UA-DM898T 15.6 inch Full HD Notebook (Intel Core-i7 7500 Processor, 8 GB RAM, 1 TB HDD Storage Drive, Windows 10) - Black

I can recommend Ebuyer, that's where I got mine.

Here's a selection of laptops between £300 & £500:
http://www.ebuyer.com/store/Computer/cat/Laptops?price=300+TO+500&456=12GB%7C16GB%7C8GB

I particularly like the look of this one for £450, which is basically a better version of mine. It's got an i5 (I've only got an i3 in mine) so the CPU and GPU should be pretty good.
I'm pretty keen on HP laptops these days, they are very good value. The design can be a little odd (I'm not fond of the battery placement) and the build quality is maybe a little poor (I wouldn't want to drop it...) but I haven't actually had any trouble with the ones I've had.

http://www.argos.co.uk/product/6536671?cmpid=COJUN&utm_campaign=11553376&cjsurferid=176003904172365192%3A90_LqBnXB1Jo&utm_medium=affiliate&utm_content=Pepper+Deals+LTD&utm_source=CJ&catalogId=10001&storeId=10151&_%24ja=tsid%3A11674%7Cprd%3A1546795&utm_term=1453124&referredURL=http%3A%2F%2Fwww.argos.co.uk%2Fproduct%2F6536671&referrer=COJUN

HP laptop
i3 6006u
8GB RAM
2TD HDD
Intel HD 520 Gfx

I've thought about the student requirements and you get a free laptop bag and it's only a 14" screen so it's pretty portable.

edit: £390

There is also https://www.scan.co.uk/

Thakns for all the help, guys. The laptop has now been bought. I've not tried out any 3D apart from Might and Magic IX (not surprisingly that worked) but seems good so far. It doesn't have an SSD (yet) so startup seems painfully slow compared to my desktop.

It is better to buy a laptop withOUT an ssd than those that do get added in the factories as in that budget class tend to be utter <censored>. You can then decide to live with it or install a nice one of a size you can live with :-)

With your budget, you can pick an i5 (6th or 7th gen) model with integrated graphics. I'm running an i3-5005U myself and handles old games very nicely, as well as some new games (provided I reduce the graphics quality in some).

Avoid anything that has a CPU starting with the number 4xxx or 5xxx, they're not bad but are old nowadays and some shops still sell them.

What did you take in the end? Care to share your laptop/specs?

Sorry for the long delay, I didn't see your post earlier! I really can't say anymore, I don't remember. It's perfectly possible that it's related to the manufacturer of the GPU. All I know is that the issue didn't occur with the Intel HD Graphics card I have now.