I would use the trains quite happily; it is quite possible to get v expensive fares but also quite easy to get reasonably priced fares; just like flying
As a visitor to the UK, a great value ticket imo is the BritRail pass. There are 2 versions, the Consecutive pass and the flexipass
The consecutive pass allows for 4,8,15,22 or 1 month of consecutive days travel
The flexipass allows for any 4,8 or 15 days travel within a 2 month period. You validate the pass, the 1st day you use it and then the 2 months time period starts
A one month consecutive pass costs USD 1259 in 1st class and USD839 in Standard class
A 15 days in 2 months flexipass costs USD1075 in 1st class and USD725 in Standard class
On a per day basis, in GBP, that works out GBP28/GBP19 a day for a consecutive pass or GBP48/GBP33 for a flexi pass
The Britrail tickets have virtually no restrictions; they are usable on all National Rail train train services ( including Heathrow Express ) ; there is no need to book in advance , just turn up and go; can traval any distance within the network as desired any day. If using the 1st class ticket, then can also use the 1st class lounges at the major train stations
They are not restricted to off peak services, so if wanting to take the peak hour services, there is no issue there
Dave