Just run with it. Pay it as soon as possible. I'm not saying it will be a problem in the future, just possibly. Its only £350, not the national debt. If you went thru vetting you would be able to either explain it or appeal a decision . The fact your here, asking advice and your bothered about it shows integrity.

It appears that you are also behind with service charge payments ? It does also appear that the lease gives them the right to charge extra costs if you are late paying. What you need to do is write and say you are asking for a breakdown of costs as per S21 of The Landlord & Tenant Act 1985 to request a breakdown of costs (also mention that as they are threatening legal action you are requesting a breakdown as the CPR disclosure/pre-litigation rules) - https://www.legislation.gov.uk/ukpga/1985/70/section/21 If you receive something back you can then use S22 to visit them and inspect invoices, etc (although may not be easy if they are not close) > https://www.legislation.gov.uk/ukpga/1985/70/section/22 Did the service charge & admin charges demands comply with the law..i.e did they include Summary of Rights ?

https://www.retirementprofessionals.co.uk/abbey-life-included-fca-annuity-sales-review/