I am a Canadian citizen and do not usually require a visa to enter the UK for tourism or a family visit. In late February, I travelled from Canada to the Republic of Ireland for work and connected through London Heathrow and was given a 6 month UK 'Leave to enter' stamp in my passport even though I was only connecting with a flight to Dublin. Once in Ireland, I was issued an Irish work permit which is valid until the end of August. I am almost finished work now and so if I want to travel to the UK directly from Ireland, is my original 'Leave to enter' stamp still valid till the end of August or was it effectively cancelled when I entered Ireland and obtained a work permit? If it is effectively cancelled, does that mean that I could then stay in the UK for up to 90 days as per the common travel area rules? I am assuming that if I enter the UK via ferry (or even by air) that there will be no border control and so I will not be able to receive a new 'Leave to enter' stamp.
For all intents and purposes your original 6 month entry stamp is still valid, as long as its been less than 6 months since you've arrived to the UK. If its been more than 6 months, your original leave to enter is no longer valid and you need to "channel hop" to France or some other country to get a fresh 6 month stamp from the UK.
The UK does not issue entry stamps for travelers inside the UK, so there's no way to do it without leaving the country. As a consolation, tickets to/from Ireland and UK to mainland Europe are dirt cheap if you don't care about the exact times/destination, so it shouldn't be too expensive.
The visa you were granted when you arrived in Ireland does not curtail the period of Leave to Enter given when you connected through the UK. The Common Travel Area agreement does grant reciprocal visa arrangements, security measures, and shared immigration data, but a permission granted by one country's authority does not invalidate that of the other.
As a non-visa national, you would need to leave the Common Travel Area before the end of your Leave to Enter period, and apply for new immigration permission. You could accomplish this by takng a short trip to France (either directly from Ireland or from the UK) and return to the UK border. It would help to have evidence of the time spent entirely in Ireland for work, so that an Immigration Officer grants entry for the period you would like.