I can't give you an exact name for either one Andrew, but I suspect that they are both Dracaenas. What is clear is that they are suffering from a dry atmosphere. The modern living room is a difficult place for plants needing a high level of humidity and one of the most common indications of low humidity is brown leaf tips and to a lesser degree browning leaf margins. If you can use an outer container deeper than the inner one to an extent whereby you can sit the inner one on a deep gravel base and add water to just below the gravel surface (the bottom of the actual plant pot), that will raise the humidity level around the foliage. Keep well away from any source of dry heat and if possible raise the general level of humidity within the room.
There are other reasons for leaf browning but I'm thinking that the above is the cause.

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The Name That Plant forum should be able to come up with the species, possibly even cultivar names.

they are definitely dracaenas, and quite well grown from the look of them. Do you feed them at all?-feeding once a fortnight from Spring will do them good.

I tend to water them daily and once a week with Baby Bio.

The current pots have space to have around a 1cm gravel base. Would this be sufficient?