So we moved into a house just like this, very very similar but a 3 bed towards the end of 2017 as first time buyers. South East. Prices will have increased.
We had zero budget for immediate improvements as we stretched to afford the house so we had to save and spend as we lived there and spent about 12 months sleeping on a mattress on the floor as we literally had no furniture(!)
We lived there for about 15 months before I had our first baby. 2 more kids have followed!!!
We are not tradies and have zero relevant experience or qualifications in DIY and aren't particularly good at DIY other than a can do attitude.
We did the kitchen ourselves buying units from selco and slabs of wood for countertops from some other supplier for a cost of about £2k and 2-3 days of labour (3 people, us and my Dad), not including planning and shopping etc.
Selco is/was meant to be for tradies which is why their stuff is cheaper but (probably still the case?) it seems to be pretty easy to create an account by providing any old details of your "business". Recommend selcos or similar if you are buying your own stuff.
We did a decent enough job of the kitchen however parts are a bit shabby / unfinished in particular the tiling (I chose tiny square, matt tiles - do NOT do this they are so hard to put up and so hard to clean - choose big shiny tiles or better pay someone who knows what they're doing!). Over years we replaced white goods as they broke down.
We paid for a full upstairs and downstairs rewire at a cost of £5-6k (in 2017). This was the cheapest we could find and the bloke obviously rushed around and little details aren't right like spotlights being not lined up at all etc, however happy enough as it was all we could afford. We stripped the carpets and wallpaper ourselves but got a plasterer to do the plastering in other rooms (most rooms in the house) at the same time as we got a fella in to replace the downstairs toilet (knocking through a cupboard and putting a shower in, tiling, paint etc) which was £8k.
We painted all the walls ourselves, which was a ballache. We got carpets fitted upstairs via carpet right which I think was £3k. Probably a rip off but we couldn't face doing any more ourselves and we were able to get them on credit because it's really horrible having bare floors covered in plaster dust. My husband laid wooden flooring (click flooring also from selcos) downstairs himself which is far from perfect but is "good enough".
We replaced, oiled/varnished and fitted all new wooden doors (also selcos) ourselves which was relatively cheap but again, more work.
Eventually went on to get the upstairs bathroom done as well I honestly can't remember how much but I want to say £5 or £6k?
Then we have had an expensive roof repair £8k, however we always knew this was coming as the roof was in a not great state on the survey. We managed to put this off for 6 years(!).
The garden we have really worked hard on ourselves it was no better than the one you've linked, but it's really decent now with mature shrubs etc. Quite poor for at least 2 years though.
It took 1 year for it to feel more like a home (painted, carpets, furniture etc) as we were having a baby we really needed these things(!). 3-4 years for the house to be okay/nice enough but this is cause we had to save for everything and also kept having children(!). It remains a work in progress as there are finishing touches we still haven't gotten around to (utility room is unfinished, some areas of skirting are not at all well done as we did this ourselves) and now things like the paint and kitchen etc really could use a refresh.
At this stage in life with 3 kids under 6 I would be very reluctant to take on such a project again, however it was worth it because of being able to afford a family sized home in a really nice area - I think of it as having saved us the stamp duty on an extra move not to mention building more equity in a more valuable house than we would otherwise have bought.