How about a chamaerops, but you would be better off planting in a big pot which they will be fine with.
The cerifera (blue form of chamaerops) is hardier than the standard green but slower growing, again it is ideal for a pot.
The Hardiest palm would be a Trachycarpus Fortunei, but it will grow much quicker than the previous mentioned and once settled in its spot will rocket.
Neater looking is a Wagnerius, a cultivar of the fortunei but has much stiffer leaves so perfect for a windy spot. They are more expensive especially big specimens.
I shouldnt think any palm would be happy in shallow soil, however a raised bed would be ideal if possible.
Google Hardy Palms or Palm House, both are uk suppliers of palms and i can vouch for the quality. The palm house is possibly your best bet as George the owner grows them himself so they tend to be better suited to our cold weather,
Palms from the likes of B&Q tend to be cheap right now, but you do get what you pay for.