I've been in the same position recently, and it was such a nightmare I eventually gave up and started looking for a flat to sublet for a couple of days a week, which happily I found really quickly.
I do think I had unusually bad luck though, so don't lose heart. I came up with a really crap cover story to explain why I was renting a flat when I had no intention of leaving my current one, and it just ended up making the potential landlords very suspicious. It was suggested by the agent, that paying 6 months up front might persuade them, but unfortunately I didn't have it.
I tried again with a second flat and, again, the landlord was suspicious, but agreed to let me take the flat. I came within a hairs breadth of signing the contract, when I found out that the landlord owned half the block, and spent most of his working days on the premises
I would do as much as you can to find out, as subtly as you can, who else lives in the block and how often the landlord visits the premises.
If you have an accountant, references shouldn't be too much of a problem. They will just ask you for a bank reference, and a letter from your accountant saying that he knows how much you earn, and has no reason to believe that you won't be able to make the payments. I rang the bank to ask them what their criteria are for a good reference, and they said only that you are either in credit or within your agreed overdraft limit, that you have regular payments going into your current account which would cover the rent (they don't bother to check your other outgoings, or anything like that), and that you don't have a history of going overdrawn without permission etc. That only leaves a landlords reference which shouldn't be too difficult to come up with.
If you are planning to rent a flat, rather than a house, don't forget that the landlord will probably only own the leasehold, not the freehold to the flat. That means that in legal terms, he is the tenant of the freeholder, and is committing an offense if he knowingly sublets the flat to a prostitute, even if she/he works alone.
If you are using a second flat for business purposes only, and no one is living in it, then strictly speaking you should be paying business rates rather than council tax. Obviously this would not be a good thing, so flagging yourself up by applying for a second property discount might be a bit risky. On the positive side, an accountant told me that you can claim the council tax on your work flat as an expense, with virtually no risk at all of the income tax people bothering to alert the council tax people
Best of luck, Anika. I hope you find somewhere really gorgeous.
P.S. If you think of a good cover story, let me know!