Quote The 55p is specifically in respect of employees claiming from their employer.
No it isn’t.
Twaddle is quite right. It's here titled Simplified expenses if you're self-employed
www.gov.uk/simpler-income-tax-simplified-expenses/vehicles
Self-employed individuals can claim tax relief for business vehicle journeys using either the flat rate Simplified Expenses method or by claiming exact actual costs.
For Cars and Vans: 55p per mile for the first 10,000 miles, then 25p per mile thereafter.
You can claim for
• cars (except those designed for commercial use, for example, black cabs, hackney carriages or dual control driving instructors’ cars)
• goods vehicles (for example, vans)
You cannot claim simplified expenses for a vehicle you’ve already claimed capital allowances for, or you’ve included as an expense when you worked out your business profits. That’s because the mileage allowance includes an element for depreciation of the vehicle.
Example
You’ve driven 11,000 business miles over the year.
Calculation:
10,000 miles x 55p = £5,500
1,000 miles x 25p = £250
Total you can claim = £5,750