Can anyone tell me how to tell what type of supply system have , it is from the 1920 .
The general impression given by what the pictures show is that you have a really old installation with hardly any circuits, in who knows what condition.
We are fitting an electric shower.
Your priority should be to get a full periodic inspection carried out.
If you can afford a shower and whatever remedial work the PIR throws up (which could be a complete rewire) then fine, but if funds are limited then you should put the shower on hold until you know the worst.
There does look to be a reasonable amount of room there for a modern CU, (but I'm glad it's not my knees and back at stake

) - if one of the metalclads can be lost a full-sized CU should go in. This could take the shower, and then be used to transfer and add new circuits.
Main thing though is to find a qualified electrician - the things you need doing are not suited to DIY. Usual rules apply for finding a tradesman - personal recommendation is always best, get a few quotes, don't go for the cheapest just because it's the cheapest, unless the difference is small etc.
You might like to consider separating the PIR from the remedial work, i.e. tell the people quoting for the PIR that they will not be getting any follow-on work, thus removing any incentive for them to gild the lily. You can always change your mind afterwards.
Remedial work, and the shower, will be notifiable, but quite honestly I'd be more surprised if it turned out that little rewiring was needed than if a lot was, so in the cost of the overall job notification fees are likely to be insignificant. If you have good reasons to prefer to use someone who isn't registered then don't let lack of registration put you off.
As a corollary, if you're having to go ahead without much in the way of references or personal recommendation, don't put any store by registration itself - sadly it is possible to become registered with woefully inadequate qualifications and zero practical experience. You don't have to spend long here to see people cropping up who are registered and "qualified", but who are clearly seriously incompetent in reality and who should not be charging for their services.
It's your money - quite likely several £'000s of it, and you have every right to ask prospective tradesmen what their qualifications are. Just being listed
here is not a good enough guide. No genuinely experienced electrician, with the "full set" of C&G qualifications will mind you asking - in fact he will wish that everyone was like you.
I feel sorry for people who have been misled by training organisations and (shamefully) the Competent Person scheme organisers into thinking that a 5-day training course, a couple of trivial examples of their work and some basic understanding of how to use test equipment will make them an electrician, but not sorry enough to agree with them trying to sell their services to Joe Public.