Just to add my tuppence worth ................. we tried exactly the same thing. Our neighbours garden was overgrown to the extent that they could bearly get out of the back door, so certainly weren't avid gardeners or in fact even went into the garden at all. We wrote the neighbour a short letter (not wanting to put the single lady under any pressure by putting her on the spot about it), making an opening offer for a rear portion of her garden, making clear that we were happy to negotiate - which would have made our garden L shaped. Unfortunately she didn't respond at all ......... so our offer fell on deaf ears........ and we have since moved. Perhaps my only word of advice (or caution) whichever way you want to look at it ............... is do try and be as careful as you can to preserve neighbourly relations ..... ours didn't break down, as she didn't speak to anyone in the first place, but would hate to think it might turn into anything ackward for the future.