I'm a certificated mechanic (engineer) in the US, and am not familiar with the regulations governing in the UK. I am fairly certain, however, that you'll be required to perform the work to the same standard as a certificated mechanic, using all the practices, publications, tools, and techniques that the certificated mechanic would have to use.
This may sound more simple than it really is. Many wheel assemblies, for example, require far more than simply unbolting and slapping a new tube or tire on. Replacement of the wheel half packing (o-ring seal), and often dye penetrant or other examination of the integrity of the wheel assembly is required, as is cleaning and a thorough inspection of all the components. It's got to be done precisely in accordance with the manufacturers approved maintenance documentation, using the tools and procedures called out for in those documents. You also need to be aware of any supplementary maintenance documentation (Airworthiness Directives, in the US, for example) which apply to that component. You may be able to do the basic work, but the examinations may require certification, specific tools and training, or a separate signoff by a certificated mechanic. Simply patching or fixing a flat generally does not suffice.
Additionally, assembly practices such as the proper torquing pattern and procedure for the wheel assembly or the final installation on the airplane must be followed exactly, with prop torque done (if I do it, for example, I need to use a calibrated torque wrench; do you have one?).
In the US, we have something similiar, which is considered preventative maintenance, which an owner can do on the aircraft. One of the restrictions here is that the operation can't involve complex assembly or disassembly, and that can quickly nullify the ability of the owner to do most operations. Even though the UK regulation is different, I'm fairly certain that the person doing the work will be required to uphold the same standards as any certificated mechanic would...right down to the use of up to date and current maintenance publications.
Maintenance is often the smallest part of the job; often the paperwork takes longer than the work performed on the aircraft, and it's going to be more closely scrutinized. Remember that whatever the regulations under which you're operating, if you touch the airplane, you're also responsible for the paperwork being executed correctly. My two cents worth.