Well, the people I used were http://middlesexcars.co.uk/. Which is a cab company local to my work which we use sometimes, and I was able to wander in and speak to the boss, and strike a deal for cash. It's not officially a service they offer.
If it were me, I'd talk to my hotel, and ask them the name of a local mini cab firm that they use, they will have at least one.
Then it's all about your ability to negotiate, and judge how reliable you believe the company to be, not always easy. However, if your deal allows for cash AFTER the event, then if they don't perform, you don't pay them... simple. If they know you are associated with the hotel, they will not want to upset you, as this may upset the hotel and cost them future business. You might initially get 'tourist rates' especially if it's a posh hotel... but negotiation, and speaking to two or more companies, will allow you to get a good deal.
Don't be too harsh in your negotiation... the deal needs to be a good deal for both sides for it to work well.
I didn't part with any cash 'up front' but the cab firm knew my company and felt they could trust me. But the client paid an agreed 'retainer' on the first day.
Addison Lee are the 'big boys' in this field in London, they are apparently very good, but may not be the cheapest. I've personally never used them, but you see their cabs everywhere.
http://www.addisonlee.com/?gclid=CPzS1sPzscUCFXDLtAodkjAAYA
I drafted a little 'contract' as I was arranging this for a friend, just so both sides knew the deal. Actually the cost was £200 per day, but I didn't negotiate too hard as I knew the guy coming was not short of money, £150 per day or less, seems reasonable for me.
Wording I used as below. I make no legal guarantees, I'm just a cautious sole who likes writing things down. The guy who used this service was very happy with how it went.
Period of hire: Saturday 29th October to Tuesday 8th November inclusive (11 days). Day rate: £200 incl. VAT if applicable. Flight details, Arrival: BA0262 12:25 29th Oct. Terminal 5 Flight details, Departure: BA0263 21:00 8th Nov. Terminal 5 Base address: ### Queens Gate, SW7 5LE. Client name and mobile: Mr #### #### – #### #### Driver name and mobile: Mr #### – #### #### Car details: Mercedes MPV
Day 1 Hours: 12:00 – 21:00 meet at Airport and transfer to base address. Then as required by client. Day 2-11 Hours: 09:00 – 18:00 at base address with final transfer to Airport on Day 11. Hours outside the above charged at £10 / 60min period, rounded up to nearest 60min. Travel to and from base address: included in day rate. Method of payment: Cash, direct from client. Deposit amount: £600 paid on the first day. Interim payment after 4 days service: £600 Balance payable before departure. Driver food and drinks: included in day rate. Fuel for mileage within the M25: included in day rate. For trips outside the M25: the driver should fill the tank before leaving the M25 area, then refill upon return within the M25, the petrol bill to be paid directly by the client at cost. Congestion charge: included in day rate. Car park tickets: parking charges should not be payable as driver will stay with the car, apart from Airport collect or drop off, where the expenses will be covered directly by the client at cost. Speed camera’s and any penalty notices: All at drivers own risk. No other charges will apply or be paid. With 24Hr notice, the client reserves the right to suspend or cancel drivers services without reason. The car should be kept clean and tidy throughout the hire period. The vehicle must be non-smoking and suitable for 6 adults with appropriate luggage.