2 week itinerary for UK

Why not fly straight into Birmingham & take the train to Stratford-upon-Avon or Oxford in order to rent a car for the Cotswolds? Air Transat fly from Toronto to Birmingham & they also fly Glasgow to Toronto - so you could save on the cost (& time) of going via London?
http://www.visitstratforduponavon.co.uk
Just NW of Oxford is Blenheim Palace (at Woodstock).http://www.blenheimpalace.com

Having done the Cotswolds (Bourton-on-the-Water, Lower Slaughter, Broadway, Chipping Campden etc.) , you could then proceed to Bath. However, beware that the main line from London to Bath is closed during August for electrification work. My understanding is that you can reach Bath by train from the west (Bristol). www.firstgreatwestern.co.uk will tell you.
http://visitbath.co.uk

It is a shame that many north Americans just go to Cardiff for the Dr.Who Experience. Within 10 Km of Cardiff city centre are 4 Castles.
www.cardiffcastle.com (in the centre). (Also visit Bute Park just NW).
Just west of the city (a 20 minute bus ride) is St.Fagans Castle & museum. http://www.museumwales.ac.uk/stfagans/visit/
Caerphilly Castle & Castell Coch are found to the north of the city.http://cadw.gov.wales/daysout/caerphilly-castle/?
Cardiff Bay is where you will find Dr.Who. http://www.visitwales.com/explore/south-wales/cardiff/must-do-cardiff-bay
http://www.visitcardiff.com

Within 1 hour of Cardiff are attractive scenic areas such as the Brecon Beacons National Park, lower Wye Valley & the Gower Peninsula (west of Swansea). This company runs guided day tours. http://www.seewales.com

It is possible to fly from Cardiff to Edinburgh - see www.flybe.co.uk
However, you may like to go by train & the shortest route is via Shrewsbury to Crewe where you change for a Virgin West Coast train.
(It is cheaper to advance book the tickets for specific trains and split the tickets at Crewe. So, CDF > CRE: CRE > EDB. You can also go via Cheltenham though this is a longer route with some trains going via York).

You might also like to consider seeing more of Wales being as you are heading north. www.visitwales.co.uk

Try & take a tour into the Scottish Highlands. Just going to Edinburgh means you are missing out on seeing the scenic areas.
www.visitscotland.com
www.visitengland.co.uk
For buses > www.traveline.info
Trains = www.nationalrail.co.uk but pre-book longer journeys with the train companies.
http://www.britrail.com (rail passes for foreigners to purchase before travel too UK - not exactly cheap so check prices for journeys first).

That seems a bit ambitious to add northern Wales, the Scottish Highlands etc., no?

Should add the time in London would also include some day trips to Stonehenge/Avebury and maybe Windsor Castle. There's plenty of stuff I want to do in London (theatre, old friends, some new sites etc.) and I don't want to drop it from the itinerary.

Scotland certainly merits a trip of its own some day - but I'd really like to see Edinburgh if I could. Maybe add Glasgow and fly in or out of the UK from there?

Did not realise that you also had things planned for London & would like to see Stonehenge, Windsor etc. That being so, you might like to confine this trip to the southern half of Britain?

You might find accommodation for Edinburgh troublesome because of the festival.

As others have commented there is nothing particularly illogical with the itinerary, but in the middle bit it isn't particularly clear where you are staying. Presumably it is Cardiff after day 6 and 7, and 'somewhere' in the Cotswolds for day 8 and 9. If you are only granting Bath effectively half a day why not miss it out altogether? Go directly to Cardiff which would be an easier journey and do more there than just Doctor Who, which won't last more than a couple of hours anyway, depending how long you gaze at the costume display at the end. The train to Oxford is also not that great requiring a change at Didcot (albeit cross platform) and you don't seem to want to see or stay in Oxford anyway. Consider going to the other end of Cotswolds and get your car in Gloucester/Cheltenham - direct trains on to York from the latter

I may have to put the trip off until September, which may be for the best.

When I'd "otherwise skip" Cardiff doesn't mean I'd only go to the Doctor Who Experience and do nothing else while I'm there! Only that I wouldn't have had it on my itinerary otherwise.

Oxford is on the agenda because I'd like to see at least one of Oxford or Cambridge and I thought Oxford was better positioned to see the Cotswolds. I know Rick has a preference for Cambridge, but my sense is you can't really go wrong with either.

I have to agree though this looks like it may be an agenda for 2 trips - and maybe stick to the southern UK (and maybe York) this time and hold off on Scotland at least for another.

Aside from Dr. Who (which we didn't even see), I loved our time in Cardiff. My husband's nan lived there until she passed so he spent loads of time there visiting her and he even lived there for a few months to keep an eye on her. I expected to find Cardiff less exciting, particularly because we went there directly from London and my husband lowered my expectations other than to say it's a party town with lots of stag and hen do's on the weekends (we visited on a Monday and Tuesday night in early December so it was quiet as a church mouse.)

The main business area was compact but open and the selection of shops was great. I am not much of a shopper and even I was a bit of a shopaholic in Cardiff. The Christmas market was small but covered the bases. Of course, we visited Cardiff Castle which ended up being the only castle tour we took during our 3 week trip. It was, as my father-in-law would say, brillant! I have great photos overlooking the city from the top of the keep and of graffiti next to the hole in the wall that was the medieval toilet.

We also took the time to walk over to the capital buildings and the university during our visit, and found a Christmas wonderland with rides, an ice skating rink, and a wooden "lodge" for drinks. One night we walked over to The Crwys for a drink before having a curry at Balti. We also had hot cider (okay, a couple of ciders) at a student bar called the Woodville after dinner. Cardiff is definitely more than just Dr. Who and a stadium!