First- try to determine what it is that draws you to the British Isles (in addition to your heritage). Do some reading, watch some films, etc. Then start to ask some questions-
How much time can you take to travel and what time of year?
How do you like/want to travel (structured, vagabond, luxury, cheap, quickly, ambling, etc.)?
Are there any special 'focus' areas for you for this trip (period(s) of history, art, architecture, etc.)?
Are you comfortable with public transport like trains and buses, do you want to drive, etc.?
What is your budget?
Then start to rough out a plan.
Just to start you off I'll offer some ideas (I LOVE the UK- have been more than 40 times, so I have a few)
If you have one week- plan on exploring London to get a taste - OR Edinburgh if you prefer to start with Scotland - you could include one day trip from which ever one you chose.
If you have 2 -3 weeks- Plan on London for 5+ days- with one or more day trips, then Edinburgh for 2-3+ days, parts of the Highlands for 3+ days, area of England between Scotland and London for several days- depending on interests, possibly other areas
If you have more time- let us know and we'll get more specific then.