In as short a time as a year, the best way to invest money is to simply save it. "A penny saved is a penny earned".
Simply not eating out all the time will save you thousands of dollars a year, which is more than most investments will earn, unless you have a large amount in an investment and have some really good stock brokers working for you. For instance, if you spend £10 on a meal 5 times a week for 52 weeks, that's £2600. If you spend £5 on a morning coffee for that same amount of time, that's another £1300.
There's plenty of other things that drain your money besides just food and coffee, but I won't get into that. Instead, I'll suggest a book to read: America's Cheapest Family. Yes, I realize that's the "wrong" country, but most of their advice can be used regardless of which 1st world country you live in.
This largish family has lived off meager means for decades and has prospered fairly well. They also help people in real life, and their advice comes from this experience as well as their own experience living these suggestions. I've paid off a fair amount of debt by saving money using their methods, so I'm another happy customer (and I'm not affiliated with them or this book in any way).
Depending on your job and your current spending habits, you might not be able to make up the missing £20k, but if you can afford a £500k house, there's probably a good chance you can. Granted, many of the suggestions in the book expect a longer term savings than just a year, but there's plenty of advice that can be done immediately to start saving money. And saving a little here, a little there, and a little in 15 other places might just get you where you want to be.
This is investing in yourself, your family, and your future in ways that the stock market can't compete.