I don’t think you can reduce by 50% for the first floor extension. It’s a myth. It’s true you won’t need more foundations, but there will be other costs (eg designing the timber frame, paying for more scaffolding).
I don’t know what are the prices where you are (I’m in SW London where everything is expensive). But I would budget £3k per metre, which for 48 square metres is roughly 145k.
Then add 20% on top for VAT. You’re now at 175k.
Also consider items such as glazing - are you planning any special windows, such as oriel or large sliding doors? Just the sliding doors can cost 10,000 or more. This won’t be included in your initial 145k.
Will you need to do any work on your existing house? New plumbing, wiring? Energy measures such as new insulation? Solar panels? That’s on top.
Are you planning any joinery? Joinery is eyewateringly expensive. Built in wardrobes easily run into several thousands. That’s per room, not for the whole house.
Will you need new furniture? Flooring? Etc etc.
You also need a budget for unforeseen circumstances. I’d say at least 20k but could easily be more.
You will need to completely redo your garden at the end, lay new lawn, possibly new paving.
And don’t forget about all the other professionals. Even if you don’t hire an architect, you will need a structural engineer (a few £k), a planning application (at least a few hundreds, probably more), possibly a party wall surveyor? Building regulations. Architect or technician fees. Project management. All of this adds to many, many thousands more.
I’m sorry for being blunt. I’m currently doing a pretty large extension (adding approximately 100 square metres on three floors, so garage conversion plus two floors on top, plus other extensions and garden room) and the costs are so far off the oft-quoted 3000 per sqm mark, that I would rather warn you. Unless you have mates’ rates, or are able to design and build it yourself, I wouldn’t attempt it on your budget.