Do you have a bank account and is it well maintained? If you have, see if you can apply for their credit card with a low limit. Use the card and pay off the debt fully every month.
Get a mobile sim on contract and pay by D/Debit. Doesn't have to be a big contract.
Takes time to build up a good credit record which is easily destroyed by financial problems, whatever they are.
There are a few firms which do cards for people with poor credit history. The ones I have seen advertised are Vanquis, Luma and Aqua. The credit limit is quite small, usually ranging from £200 - £1500.
It's going to be hard, Tinks. My OH was refused a credit card because he'd missed one phone payment. It wasn't because he couldn't or wouldn't pay, he was disputing it and cancelled the contract.
He has 4 healthy accounts with the bank that refused him. The computer said no.
With 'unpaid' debts would suggest a copy of your credit file and see who you can pay and get the debt listed as settled on your file.
I meant change your existing mobile contract not take on another debt.
Your bank will be aware how well you maintain your bank account and may well be more likely to offer you a small credit card. Weekly shop settled each month sounds good. I use mine to buy my fuel and settle monthly.