Hey OP,
For full disclosure I am a Chartered Architectural Technologist. I do these sorts of projects every day/week/month for the last 15 years. The comments below are my opinion, they will seem a bit self serving, but they are 100% honest.
Definitely get someone to do your drawings. Feel free to use an RIBA or ARB registered Architect (both websites will give you links to Architects) but you will usually pay a premium for this compared to other options.
Using an Draftsman, Architectural Technician, Architectural Technologist will generally be cheaper.
A good set of drawings will help you plan, cost and consider options you might not have considered. For example, a proposed 3m rear extension and the neighbour having one built 15 years ago seems great - but perhaps there is an Article 4 Direction on you property that means you always have to apply for planning. Also planning law changes. What if a shared drain runs under your extension (you have mentioned a manhole) - you might need Anglian Water approval in advance to building. Some shared drains mean you can't build within 3 metres or even 6 metres of them!
In my opinion there are too many "what ifs" to ever do an extension without drawings. Get someone that knows what they are doing to hold your hand through the process.
I don't know where you are in the country, but if you costed out £2000 plus VAT per m2 of proposed footprint, then you should be OK, but your choice of kitchen, amount of work to the existing, any work done by yourself etc. might push that up or down.
IMO the best way to find someone to do your drawings - is word of mouth. Find out from friends, or that neighbour of yours, who is any good, based on completed projects.
Good luck.