I am excluding from my answer new synths with built-in keyboards. That would broaden things too far into the area of product-recommendation. Suffice to say there are lots of MIDI keyboards on the market, and all of them will function as a MIDI sound module if you want to control them from a different keyboard.
Other than to say you want to play 80s music, you don't say much about what kind of sounds you want to produce -- and that's going to play the biggest part in what you want to buy. Bleepy analogue solo sounds? Warm analogue bass? Lush pads? Cheesy FM leads? Do you want high quality presets, or do you want to craft your own sounds? These are all factors that will influence your choice of synth.
In the words of a forum post I found somewhere, "software synths have pretty much taken over the low end world". £200 will get you a laptop that's more than capable of running most software synths. The cheapest Dell/etc will do. A second-hand laptop a couple of years old will also do the job.
In Windows, there is a wide range of software synths provided as VSTs - a standard plugin format. Many VSTs are free, or just a couple of pounds -- although there are also VSTs that cost hundreds of dollars.
You plug your VST into a program that can host it; and there are many. One such is VSTHost, again free, which takes a bare-bones approach to routing MIDI notes to VST sound sources.
There are similar tools for Macs.
This approach gives you lots of flexibility to try different types of synthesis. Unlike a hardware synth, which does what it does and nothing else, your laptop can be a twittery analogue synth one minute, an FM synth the next, a sampler the next, or all of them at once.
If your keyboard has a USB socket, then you're ready to go -- the sound will come out of your PC's sound card.
If your keyboard only has a DIN type MIDI out, then you'll need to buy a hardware MIDI interface, and now you have a choice -- a cheap one that just converts MIDI to USB? Or a posh sound card with MIDI as a bonus? See How necessary is an USB Audio Interface?
You can also hook up your MIDI keyboard to an iPad, in which case there's plenty of soft synth apps, including the bundled GarageBand and the excellent Sunrizer.
If you are dead set on using a hardware sound module, without a built in keyboard, you will probably find yourself restricted to high-end rackmounts that are out of your price range, or second-hand modules.