A credit check is a credit check, their scoring system see's you as too much of a risk im afraid, so you won't have any more luck by going into a store and trying - just embarrasment if anything. It also does not look good on your credit record if you try for credit twice in quick succession with the same company, and also if you get rejected twice.
The easiest network to get a phone on if you have a bad History
, is supposedly Orange.
On a sidenote, the £100 is a deposit, that is refunded after 3 or 6 months, to ensure you pay your bills - just like when you pay a deposit to rent a house etc... I also doubt you would get a contract-standard phone for £100 on PAYG, nevermind free, not to mention on contract you have the massive advantage of inclusive minutes, text and web etc...
Also, be careful what price plan and phone you are trying to obtain, as you have said you have a bad credit record, you can't be looking to take the latest and greatest iPhone on a £50 a month contract, because all networks would say no to that (even moreso on an iPhone due to the revenue they are contracted to pay to Apple). Go for a low contract and a lesser phone to begin with.
Im not sure if sim-only contracts have a different credit scoring points system.