Sorry but i'm not doing the job you are paying an agent a fee to sort for you. I have given you a lot of good examples. You need to take time and research what would work best for you both in terms of quality of course and value for money.
The vast bulk of the UK University terms start Sept/Oct in the year. This is in line with the UK academic year. Very few offer a January Intake. Also as stated your exam results are the key to unlocking which universities would take you.
If i was in your position as you are leaving this until so late in the day to apply, i would be looking to apply in January 23 for the 2023 year starting Sept 23 and likely pick somewhere like Chester to do it.
Good luck in your quest...