Yes, but the higher voltage cables have an earthed armoured screen which minimizes interference.
woody, you should be OK for that distance. Test before you put the floorboards back. If necessary, it should be a few minutes job with an electric drill to make additional small holes.
Problems only really become apparent if the phone is an extension on an electronic 'call connect system', as used in offices, etc., and the mains is feeding an inductive load such as a fridge, photocopier or fluorescent light. Then symptoms are not interference you can hear, rather erratic behaviour of the system, calls cutting off, etc.
From click here Although this relates to data networks the same principles apply to voice networks.
Cable routes should be planned to avoid fluorescent light fittings and power cables (exceptions can be made in the case of optical fibre). They should not be run in the same conduit as power, or the same channel of a trunking system, and where they are run parallel to power they must be at least 60mm apart (BS7671-92) . Crossing power cables is allowed but it must be at right angles, and some form of bridge should be used.