I've been on two P & O cruises and the shuttles into town have always been fre.
Went last year to some of the destinations, transfers available either free or 1 euro,Oslo dock right in the centre, Tallin shuttle bus, Helsinki and Copenhagen public transport very frequent from dock sid.
Hello P & O are notorious for charging larger amounts than €1 for shuttles and they charge whenever they can. Sometimes the local authority put on free transport but P & O always give you the impression that they are supplying it FOC. Yes P & O shuttles are available and you normally have to buy tickets on board then go to the bus unless they have changed their systems....Heathe.
If you don't mind walking a mile or so on the flat then Copenhagen city centre is also a walking option. The Little Mermaid is quite close to where the ships dock but would be missed out by the shuttle bus run. To be honest I found it a bit disappointing but it's en route from the ship to the city centre when walking and you save all the hassle of 40+ people getting on and off a coach for a quick photograph. Walking on from there you find some very nice squares and public buildings which you would otherwise miss on the shuttle. Tallinn is also walkable from the ship but ideally you would get driven to the top of the old city then walk back down. I recall that most shuttles drop you off at the old gates at the bottom of the hill. In Helsinki I purchased a day ticket for the buses which got me out to the museum of old buildings on the outskirts of the city (where a lot of tours go to) It's only about a 15 minute run but check the timetable for frequency of service and lunch breaks.
Sailed on Arcadia in Oct. 2007 shuttles were plentiful and free to center of destinations.
I went on this cruise last May. Only booked excusions in St Petersburg. At most other destinations a shuttle bus is provide either free or at nominal cost. At Copenhagen a public service bus from the terminal is available. Go to Tivoli Gardens and walk back thro the city a lovely stroll. You don't need any transport in Oslo as you dock right near the city centre. The same is true at Tallinn you are right near the railway station and you can take one of the frequent trains into Rostock nearby. If you areafellwalker you should have no trouble walking to the centres of Tallin and Helsinki from the boat although a shuttle is provided (at a cost).