Hi OP
Apologies if anything seems like stating the obvious - you mention that you are Irish so I am trying to include as much info as possible in case you are not familiar with the UK tax system and I don't know how it differers from the Republic of Ireland (sorry I assume you are from the Republic apologies if this is wrong).
. How long have you lived in the UK and how long has your DP being doing this sort of work?
Unfortunately, it's shit in the construction industry in the UK. There is plenty of work but no job security and a lot of middlemen taking a cut of the workers' wages.
My DP has various jobs but in the winter works as a plant driver in the building industry. He gets all his work via employment agencies so your DP needs to get himself registered with a few of them in your local area.
I think my DP got names of agencies via the job centre but googling brings up Agency Central so perhaps look there to find ones that operate in your area and trade?
Luckily he is in the middle of a contract that will last at least 5 months, maybe longer but he gets lots of texts from the agencies offering other work.
If your DP has a UTR that means that he is registered as self employed with the UK tax office, but that does not necessarily mean that he is legally considered to be self employed. That is for HMRC to decide and there is a big problem with False Self Employment.
He may be registered with the CIS scheme where they take 20 or 30% of wages for tax. This is because in the past there has been a big problem with tax avoidance in the construction industry .
If he has a UTR he needs to do tax returns and he also needs to look at what has been paid in his name via CIS because he may be due tax back as they don't take account of your tax allowance and the tax rate is 20% unless you earn more than about £42k pa.
Once you are correctly registered with the CIS scheme (there seems to be a couple of steps and if you don't complete step 2 that's when they take 30% not 20%), you can see online on the HMRC website when you do your tax return how much tax you have paid. The lack of pay slips is worrying - he should be getting some written advice about his pay, but that might only come after the end of the tax year on the 5th April. Thinking about it, my DP didn't get written advice when he was on CIS but they sent something at the end of the tax year and it was all there when he did his tax return, so maybe this is standard practice.
The other way that he might get paid if he does agency work is via the umbrella system which is also shit. Full details here. This is the response to the workers not really being self employed and the umbrella companies take a cut of their wages.
It may be possible to set yourself up as a limited company to avoid being on the umbrella system or try to get on PAYE with the main contractor or subcontractor but the limited company route is expensive and not worth it unless you earn more than about £25-30k I think.
I also suspect that there is a lot of back scratching between the employment agencies and the umbrella companies so you pretty much just have to accept the system or not work.
The government also keep cracking down on all these things because the workers are effectively unwilling participants in a great tax avoidance scam, but that's the way it is at the moment.
DP is just sticking with it and trying not to worry about all the above because the alternative is NMW shop or factory work, which pays less and he hates - he likes being a plant driver and earns reasonable money from this.
To get into this was surprisingly easy too - he did a free 2 day course for one machine and paid £200 to learn to drive another machine and now has always had work when he has needed it in the past 2/3 years. Was harder at the beginning as he had no experience, but once he had got experience it has been fine.
Good luck, HTH, and on the bricklaying front, I can only suggest that your DP talks to the bricklayer bosses on site to find out if there are any vacancies and whether it would be worth saving up to pay the £500 to get the right tickets once he is back in regular work?