Doing the UK & Ireland in one go is a bit much and you will probably not be able to take your car across the Irish Sea – so would need to hire 2 cars.
You will not find all stop junctions like you have in Canada. Neither can you make a turn (right in Canada) when held at a red light. On roundabouts, you give way to traffic already on the roundabout. Roads come in 3 main categories. Motorways (M) are long distance divided highways usually with 3 lanes each way. The next category down are ‘A’ roads and some of these are also divided highways. Next come ‘B’ roads which can best be regarded as good country roads. Country roads may only be wide enough for one vehicle – so you may have to reverse to the nearest passing place. Many of the roads evolved from medieval tracks so you can expect far more bends than is the case in Canada. Towns were also built long before the car age so in many shopping streets, cars have been banned completely. (You will probably find this a pleasant experience). That said, on the edges of towns, you will often find retail parks & supermarkets with extensive free parking – just like you have in Canada. Such supermarkets are the places to fill up with fuel as places on the motorways or the middle of towns are dearer. The supermarkets also have toilets.
On motorways, the speed limit is 70mph – yes, the Brits are old fashioned – still have distances in miles. Odd as just about everything else is metric including fuel being sold in litres (for price). Most other roads have a limit of 60mph unless a lower limit is shown. Where you see a white circle with a black bar – it means the 60mph limit applies – unless it is a dual carriageway – when the limit is 70mph (unless lower limit shown). Oh, and on multi lane highways, you must over take on the outside (to the right) of slower moving stuff. http://www.highwaycodeuk.co.uk
You should specify that you want an automatic – otherwise, you will get a manual transmission.
I would suggest that you look at Google Earth & zoom down to have a look at the places where you might go. You could even drag down the yellow man to see the streets & ‘drive’ along them .
Great Britain has an excellent train network which you also might like to consider using. The following link will tell you more:> http://www.seat61.com/UK-train-travel.htm#.Vwn_TOlVuiY