By train to Peterborough
Peterborough is a major train hub and well connected with many parts of the country. This feature it shares with few other places of similar size in Britain makes the train an obvious choice for your visit to Peterborough. Regular services to London, Stansted Airport, Birmingham, Norwich, Scotland and the industrial north are available. Services to nearby places such Ely and Cambridge are more frequently while the service on the line to Lincoln is just horrible. The train station is located to the southwest of the city centre. The Cathedral is a 10 minute walk away, the big shopping mall less than five.
A choice of companies
GNER trains ('the route of the Flying Scotsman') leave from King's Cross and arrive in about 50 miutes to an hour. They are fast and comfortable. Some service use redundant Euristar trains.
On the downside they cost the earth.
I'm afraid the alternative is a bit ropey WAGN (pronounced 'waggen') have some knacked old coaches that trundle up to Peterborough in about an hour and 10 minutes.
They are cheaper - and damn well should be. They also leave from King's Cross, usually from platorm 9 or 10. UPDATE : Now called some new silly name, like Capital connect express or something, but it is still the same crowd.
NB look out for the Harry Potter plaque as you walk through from platform 4 at King's Cross.
Good connections east-west (sort of)
Unusually for Britain, Peterborough unlike many other places of a smilar size has relatively good east-west connections by all forms of transport.
By road the A14 (passing by Huntingdon) is very useful for Birmingham or the East coast ports
By Rail there is a regular service East to Stansted Airport and Norwich/ Ely / Cambridge
Going West there are regular services to Birmingham and Manchester.
By Coach a regular service connects Eastwards to Wisbech, King's Lynn & Norwich
Going west there are regular services to Leicester.