Also - please, please, please brush up on HMRC/tax/PAYE rules and regulations. I have worked for so many companies and there hasn't been one where the HR person understood my tax position. I have had to send countless emails and explanations asking them to work out how to assign my tax code and ensure everything is correct. One didn't know what to do with my student loan. It's the basics of HR, people!!
Tax / HMRC / student loans is not for the HR manager to sort out. If there is a payroll department then the payroll manager will know this information. It is impossible, IMO, for HR to know the ins and outs of this very specialist (and changing) area. I would go as far to say that each individual is responsible for their own tax / HMRC issues. Decent payroll managers will help with the explanation from HMRC, but ultimately they input the information on to the system.
treacle HR assistant and admin jobs come up rarely. I have found they are filled internally, by people who know the business in an operational capacity, or as an internship / placement (I started out like this). I'm now HR Manager for a medium to large sized business, which is part of an international business and I haven't seen one HR Admin role advertised externally. Even my own department, I recruited within.
HR service centres have HR Administrators, very low paid roles but it is a foot in the door. So you could target head offices and sell certain transferable skills. Happy to review your cv and make it more transferable.