The general (unofficial) rule is that you should only return to the UK after spending the same amount of time outside of the UK as the time spent on your previous visit (which may be less than the granted leave to enter).
Immigration Rules - Immigration Rules Appendix V: Visitor - Guidance - GOV.UK
Genuine visitor requirement
V 4.2 The applicant must satisfy the decision maker that they are a genuine visitor, which means the applicant:
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(b) will not live in the UK for extended periods through frequent or successive visits, or make the UK their main home; and
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(e) ...
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An existing leave to enter is not effected by a stay in the Republic of Ireland. (CTA rules: Exemptions from deemed leave on the basis of specific status).
It is up to the discretion of the Immigration Officer to grant a leave to enter.
Even if you do not overstay by a few days, any return before 6 months may be denied since it would look as if you are trying to stay for a prelonged period after just spending 6 months in the UK.
Returning after 7-8 months, the Immigration Officer may see the overstay of a few days but may choose to ignore it if they have the impression you are not trying to stay for a prelonged period.
The situation would change if you were found in the UK while overstaying.
That would have a serious effect on any future reentry.