Upvote:2
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.
Upvote:3
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 If its been more than 6 months, your original leave to enter is no longer valid and you need to "channel hop" to France or some other country to get a fresh 6 month stamp from the UK.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.