It's possibly a little early in the year to plant fruit trees if the ground is sodden or frozen, Steve - wait until early spring. In the meantime, you can buy container-grown rather than bare-rooted ones. A maiden or two-year old tree is unlikely to give you any fruit this year, but you can get older trees (at a price) which should establish themselves quite quickly.
It depends on how much space you have and how tall you want your trees these are guidelines for apple trees:-
Rootstock M27 is the dwarfest, for growing bushes, cordons and fans. Begin fruiting when 2-3 years old
M26 is dwarfing and will get about 10' tall, and carry a reasonable crop of fruit after 3-4 years.
MM106 (what we have got) is semi-dwarfing and will grow up to about 14' tall.
MM111 is for tall, vigorous trees - probably too big for an allotment.
These last two will carry a few fruit but won't start cropping properly for 5-6 years.
There are nurseries where you can order varieties specially grafted onto whichever rootstock you want, but it's too late for this year, I think.
I imagine the scenario is similar for pear trees.
I'm sure there will be a good choice at your local garden centre, but if you want to be more adventurous and get some professional advice, have a look at www.bernwodeplants.co.uk . I'm not necessarily suggesting you buy from them - they are a fair step away from Yorkshire, but it interesting to see so many varieties listed, with their pollinator groups, descriptions and instructions. I have one of their catalogues which I use as a reference book.

what a brill answer Gattina, my brother was asking me so I can now point him in the right direction.

As Gattina mentioned - don't forget about pollination as well. There are self-pollinating varieties but as a general rule you need other apple trees in order to get fruits. Or check if there are any within close distance.
There are also fruit trees called 'a family trees' - few varieties grafted on one stem - perfect answer for the pollination:)

The problem with "family trees", Kasy, is that one of the varieties often tends to be stronger and more dominant than the others, and takes over the entire tree.

I have never grown them so really can't say much about them. And I am not big fan of hard pruning either.

As the allotment is not yours for ever and does not have the same protection as a garden, I would consider the cheapest option which would be buying bare-rooted trees from the supermarket or DIY stores. They can be grown as cordons and will take up very little space. As keen as you might be to get a crop off of your trees, you must be prepared to pick any immature fruits from them during the early years as you need to let the energy go into producing branches and roots. The only drawback will be that you probably have missed the boat until next year to make your purchases.

I planted a Pear Tree on my allotment and have only had one crop in 3 years, because I didnt go down when it was in flower and cover properly to protect when frost forecast.
Unprotected Apple Trees were in flower along on other plots at the same time, and not affected at all. I took an old duvet down 2012, it was of no effect, just got 2 pears.