Don't worry Adella, it's not as bad as you think - if your garden really is north facing, you would only have a strip of sunlight at the top end at this time of year. But just watch and wait - by midsummer, the whole of your garden will be in sun, and it'll stop short at the house, never get into the rooms which overlook the back garden. In a month, you'll notice that that strip of sunlight is now halfway down the garden, or at least a third down it, and it'll progress like that. The only thing I don't know is how narrow your garden is - if its very narrow, the shadow from the garage wall may keep some of it in shade. If its not particularly narrow, then just work out as the year progresses which parts are shadiest (probably be the left hand side, which should get morning sun and be in shade by about lunchtime).
This means you can plant most things without any trouble, excepting if your garden is exposed to northerly winds, but as you're in Middlesex, I'd assume you may be surrounded by other gardens/houses, so this shouldn't be a problem either.
If you still want suggestions for planting, it'd be helpful if you could post a photograph, or tell us what's in the garden currently.

Variegated ivies trained against walls or fences in shade look nice in my opinion. Hardy Cyclamen love shade and flower from the end of autumn (C. hederifolium) to spring (C.coum). Hellebores are out now and do well in shade.
Click on "S" at the bottom of the page and go to "Shade plants" for more idea.
I think you'll have a variety of situations, with some giving opportunities for plants that like more light as well.

The answer from Bamboo is correct. I too have a north facing garden but can grow virtually anything and everything. Its not a big problem. Enjoy your new garden .

Thank you all for your advice!

The rule of thumb I read in a Roy Lancaster book is, if you look up and see the sky, then it is part shade, and there are a load of plants that will take that amount of light.