I used to recommend this step as essential, but given the fact it can be a struggle to get your elected representative to input usefully, I now only recommend bothering if one or several of the following apply:
Otherwise it can be more work for not much gain, unfortunately. But we have lots of evidence that active involvement of your MP goes a long way to a successful outcome. Actually the minimum you need them to do is use their letter-headed writing paper, as it does seem to make a difference to how cases are handled.
Your MP does have to act on your behalf if you ask; it is their duty. They have access to a specialist MP Tax Credit Hotline to help them deal with your case more quickly, so tell them to use it. (MP's are very hesitant to use the their exclusive phone line dispite the desperate and urgent situations of the constituents.)
If your MP does not act on your behalf, advise them that you will make a complaint against them. It’s probably quicker and more convenient for you to deal with your MP, or their staff, via telephone or email. Both contact details should be freely publically available - to find out who your MP is go here: Find Your MP.
At this stage the MP will probably want to have one last try to reason with HMRC and will therefore write to HMRC on your behalf. This isn’t strictly necessary, but let them; if they do it they are being helpful, as long as the situation isn't currently urgent.
Otherwise ask them to forward your dispute to The Adjudicator's Office (not the Parliamentary Ombudsman, which is a possible later step).
Like I mentioned it isn't essential to involve your MP, so could always move on to The Adjudicators Office stage (our Dispute Step 4) on your own.