Hello Alison,
The north-easy facing site rules out a number of possibilities, you will not get long periods of sunshine therefore reducing the flowering performance of most of the sun-loving flowering climbers.
I would suggest you consider the following plants, that I think will thrive despite the reduced light levels. The first two will provide leaf colour/interest rather than flower colour but I would always choose the former because it is usually on a larger scale and tends to last for a longer period:
Parthenocissus
Euonymus fortunei
Lathyrus latifolius
Any of the climbing honeysuckles would also be suitable, the reduced sunlight would limit aphid attack on these which can be a real problem in much warmer, sunnier sites.