I take it you are not registering this business as a Limited Company.
You can (and should) register as self-employed with HMRC and keep records of the business - incomings and outgoings. One of the outgoings will be the rent you pay to your MiL but I don't know how you/she can reconcile this with the no sub-letting bit. Unless the turnover of your business exceeds about �61k pa you don't have to be registered for VAT. As a self-employed person you are assessed for tax annually and have to complete an annual tax return. These people also extract your NI contributions.
The only other potential hassle I can think of is HMRC claiming you are not self-employed, but in fact an employee with a contract of service from your MiL. This is called IR35 by HMRC after the circular that introduced the rules and it has potential cost implications for your MiL. Ask your MiL about it - because most hairdressers working in salons seem to be self-employed these days and seem to be avoiding any IR35 type claims from the Inland Revenue.