If your landlord won't carry out repairs they're legally responsible for under Section 11, you do have the option to get the work done yourself and deduct the cost from your rent. But this is risky if you don't follow the correct process, because your landlord could treat the deducted rent as rent arrears and pursue possession proceedings.
The process requires several steps. You must report the repair to your landlord in writing, giving them a reasonable time to respond. If they don't respond, you must write again, stating that you intend to arrange the work yourself and deduct the cost from rent. You should then obtain at least two written quotes from reputable contractors, send copies to the landlord, and give them one more reasonable opportunity to act. Only after all of this can you proceed with the work and deduct the cost.
You can only deduct the cost of repairs that fall under your landlord's legal obligations. You can't deduct costs for improvements, for damage you caused, or for work that isn't the landlord's responsibility.
This process is a last resort. Reporting to the local council for an HHSRS inspection or taking action under the fitness for human habitation legislation is usually a safer first step because council enforcement doesn't put you at risk of rent arrears claims.