I believe you should be able to travel from London to Manchester without any changes and would be about 4 hours max. You could take a flight which would be about an hour from London to Manchester, approximately £70-£80 (depending on luggage)if you can go with Flybe, Easyjet would most likely be a little cheaper. And, yes, it is safe, of course.
Google "Madam Tussauds". It is probably best to get tickets in advance if you can and be prepared for extremely long queues.
If you are intending to visit areas beyond the major cities, there is Stonehnege and, in Portsmouth there is HMS Victory (Admiral Lord Nelson's flagship), HMS Warrior, The Mary Rose (Henry VIII's flagship), etc. Brighton and Windsor seem favourites too.
RE: How do you like your toilet paper to come off the roll...
Amongst all the drivel, we were desperate for an intellectual thread....Thanks!!