The second photo - on the trunk, there are two darkened areas running horizontally where it looks as if fluid might have been trickling downwards from inside the trunk. Is this just a trick of the light in the photo? If its not, is the trunk soft anywhere in those areas?

The first photo shows a different palm like plant, but its taken so close to show the damage I can't decide what it is - the first photo is likely a Cordyline, but I'm trying to decide if the variegated leaf one in a pot is a Phormium or Yucca... do you know what it is, and if not, can you add another photo showing the whole plant, preferably including the pot. One thing I can say is there is a snail hiding in the leaves..

Sorry for all the questions, but they're important to try to decide what's going on..

The grubs and all that jazz are secondary problems. The London climate really isn't suited for these palms. You can successfully grow these palms as indoor houseplants if you have the space and could install indoor growlights. Then just move them outdoors in Spring & Summer. 'Cold' & 'wet' are not what they want. Hot, 12 hours of full on strong sun, dry, sandy, arid are what most palms like. They like tropical beachy like conditions like Miami & Hawaii. Even under ideal conditions, palm trees of all types around the world are dying out because of blight going around. Many palms are in danger of extinction. Several lethal diseases are taking out palm trees rapidly worldwide and experts are baffled. It could be due to climate change, etc. There are 3 palms that can grow in London - Read this link to find out which ones.

http://www.plantpost.co.uk/palm-tree-uk.php#.YTeUxdQwjGh

The large palm in the ground does seem to be Cordyline - these grow all over the south of the UK and near the coastline with no problem, unless we have a very severe winter. They usually survive for around 30 years in average conditions, in very good conditions, up to 50 years. There are pests that affect them - mealybug, scale, aphids, spider mite, though the latter is only a problem in hot, dry summers - see link below for more info on pests plus how to treat, but the trouble is, reaching the leaves to spray them won't be easy

https://horticulture.co.uk/cordyline/

You could just cut it down lower instead next spring around May, at an angle and let it resprout, which it will, if its too difficult to reach the top and it looks worse next year.

The one in the pot, though, looks as if it might have variegated leaves, unless this is a result of problems its suffering - if the leaves are variegated, it won't be a Cordyline. It looks like it has a bad case of Phormium mealybug, which primarily affects Phormium, but can also attack Cordyline, though I've never seen it on one - it can be treated with a spray that treats for this specific pest, but does need to be sprayed as far into the leaf bases as possible because that's where they live.

Thanks everyone for your thoughts. They are really helpful.
I will go through the possibilities and also get some appropriate spray, and contemplate a cut back. I did have it pruned last year, which also made worried that this was a reaction to a prune and that maybe I
shouldn’t have . But it was with a proper tree surgeon and he agreed they needed cutting back at the time.

Thanks again, hopefully I won’t have more questions.
Faye