Using Concepts on an iPad to sketch out some ideas..
Permitted development allows for single storey extensions up to 3m on a semi detached house. Max 3m high to eaves. Party wall notices may be required depending on how close you are to the boundary with your neighbour. All straight forward work.
(Permitted development allowances did allow for larger extensions through the neighbour consultation scheme, but they need to be finished by the end of May this year to comply – no news so far as to whether they will extend this neighbourhood consultation.)