I think that everyone may have a different opinion of a cheap hotdog.  You can purchase local varieties of hotdogs costing as little as 10 for $1.00. A local wholesale clubs sell a package of 100 hotdogs for $9.99 plus tax.  You could probably build a hotdog for around $0.35 each and retail it for $1.00 and still make close to a 3.0 markup. On the other hand an Oscar Myer 100% beef cost almost as much as a Sabretts 100% beef so the final retail cost would be the same for these two dogs. The Sabretts blows away the Oscar Myer.
Again, from my experience only, people will pay $2.00 for a decent hotdog. You may be right about hotdogs not being a tradition in London, but remember you want your customers to happy with their purchase. If I went to the local pub a bought an English Ale that was a little flat then I may not ever consider buying another one.
If anything I would run specials to get you customers acquainted with Hotdogs and build your business up from there.