So, I would like to get started in mining BTC and live in Britain south of Cambridge. I have a custom machine running an OC 7870, intel i5 etcetera. Would it be pointless mining with this hardware as I only get about 380 m/hash and is this too low in comparison to electricity bills. What's an Asic Miner and is it worth buying one of the £40 1.6 GH/s ones. Will this be too expensive in comparison to my electricity and how much could I make off of this in a month including the price of the electricity?
Yes, GPU is out of the question for Bitcoin. Although, you could mine Scrypt Alt-coins with it, like Litecoin and Dogecoin. As far as your ASIC is concerned, you can input your numbers in the Profit calculator at http://mining.thegenesisblock.com and see what you come up with...
The most profitable form of mining now is actually alt coin "scrypt" mining. So most efficient investment would be to get some good GPU's for alt coin mining, go to http://www.coinwarz.com/cryptocurrency then pick one of the top coins that has decent volume. Then start an account with a site like Cryptsy and trade those alt coins for Bitcoin.
Kind of complicated but much more profitable for investment size then Bitcoin mining. Doing this and getting lucky with mining a few coins early before difficulty took off has netted me a little over 2 Bitcoin in 2 months with a 1000 dollar investment. Your results may very however as there are a LOT of variables to take into account and these alt coins can fluctuate even more then Bitcoin.
If your dead set on BITCOIN mining then I would suggest something like an ASICMiner Block Erupter Cube 30GH/s to 38GH/s Miner http://www.amazon.com/gp/offer-listing/B00H8K3MZU/ref=dp_olp_new?ie=UTF8&condition=new
I will warn you that with Bitcoin mining and difficultly increase that with that miner there which is one of the best deals I can find you will be lucky to make your money back at current prices.