One of the best ways to avoid having to go through the process of mortgage finding and house purchase is to just look at developing the home you are already in. If you are in need of some more space (one of the most common reasons why people move in the first place) then an extension might well be the answer. You don’t even need to have a brick and mortar one. Take a look at Oak Extensions like the ones that you can get at https://www.timberpride.co.uk/oak-frame-extension/ to see what options there are.
There is a bit of work to do before you can go ahead and just order one. As it will be over a certain height and length it will need to be approved by the council planning department. Try not to view this department as obstructive. They will only say no to something if it is not a feasible option or create a problem for your neighbour. On that point you could discuss this with your neighbours first. An official notice will go up in your property as to what you are planning to do and they will be written to anyway but a more informal chat is a more neighbourly thing to do. The main sticking point is the “right to light” rule. You can’t have anything that casts shadow over the other garden.
Once you’ve got the Ok from everyone (they get some time to respond) you can start on the work, or the professionals do. All you have to do is decide what is going into it after it’s done! However, that’s another story.