We did - and we're on track for a £100,000 turnover in our first year's trading. BUT - we knew exactly what we were doing, had previous experience of running our own business, had important contacts in our chosen field, and a known track record.
Have you produced a business plan? If this is to be a 'proper' business (and not just a hobby that happens to make you some money) then you need to start at the beginning.
What is the bare minimum that you can live on? That is the amount that your business will have to be making from the get go, unless you have savings you can live on.
Don't be under any illusions about how much it will cost to set up - we had spent £6,000 on the business (this figure doesn't include any rent or stock!!) before we got our first payment in. And we had been trading for 6 months before we were able to pay ourselves a penny.
To answer your question - yes, it can be done. But it isn't something you should enter into lightly. Get advice (accountants are your friend!!), don't be afraid to ring HMRC if there's anything you're not sure about (I find them much easier to get hold of on the business side of things), read 'Setting up your own business'-type books, and if you don't know how a balance sheet works, start learning. As regards the present economic climate, some industries do better in a recession - on a trivial level, people buy more baked beans!!
What line of work are you wanting to get into?