The silver birch looks as if it has a bend on the stem and ? a low side branch?. If this is the case, is it worth keeping? Also, allow for the fact that a mature silver birch can reach 30m and they are often quite brittle in very frost weather. (My part of W.Sussex lost a good 50% of its SB during the winter of 2010/11. The water in them froze and they just snapped off under the weight of the snow and ice.) If it is then how about a low raised border to help the roots. 4-6" deep would be sufficient. Obviously you would have to put protect the fence,as opposed to putting earth right up to it. A raised border would give you a better border with more choice of plants - SB will grow in any pH soil so you could even change the soil in that part of the garden.

Hi. I think pruning the roots on a birch tree would be prohibitively expensive( and probably pointless). Ideally trees need to drop their own leaves onto their own roots and for nature to take its course in terms of temperature control and moisture retention etc. As soon as there is human intervention the roots will suffer, from compaction, dehydration or just severance. Certain trees will 'put up' with interference better than others. Birch is a colonising species and therefore fairly tough. I think your options are as follows; cut straight through the roots and take a chance that the tree will be unaffected. Stop the edging where you have and start again a similar distance the other side. Or you mention slabs to the lawn edge? if you are laying them horizontally as in a patio, lay the ones over the roots on sharp sand or a very lean mix of sharp sand /cement. If you are using 100mm x 1000mm slabs as edging, get a local builder to cut one piece lengthwise and don't dig it in so far. The last option is the preferred one and will appear visually the same as the others. Brian