Ok firstly I will say I am not in any way an accomplished bushcrafter especially since discovering this forum where there are people with a wealth of experience who are friendly and offer free advice, that said I have done some hiking in my time.
Apart from trips in and around the UK I spent 6 days hiking through the Jungle of Mexico (not as extreme as it sounds... it was a guided trip along established trails with camp points on route) still hard work but great adventure.
When I was much younger than I am now (jeese that sounds bad I am only 39) I did something not as extreme as you are planning but I grabbed my rucksack packed my camping gear and hiked/hitchhiked from Berkshire to Southern France and back with a mate so I do know a bit about getting up in the morning packing up and carrying everything with you on your back for days on end... I would say some of the best advice you have received here is don't just buy something on line because someone says its good.. If you look at most comments they say "I like it" or "I don't" not go buy it.
That is because everybody is different and all our body shapes differ. What one person finds comfy another finds annoying (for instance I don't like "war belts" I find they irritate me with a pack and can become quite sore after a while, just my preference)..
Anyway I digress the best advice is don't just buy something on-line.. Go try it on (you can always find an online deal when you know what suits you). You are going a long way and wearing something that is comfy is so important... I cannot stress that enough! There is a reason things hurt.. They are not suited for you, not a problem over 3,4 or 5 days but day after day they will start to put you at risk of injury and you seem pretty focused on this so do it right and don't end up coming home after 3 days because you've damaged yourself!
In sizing your pack take the most you can carry
comfortably and plan you route stops and rests accordingly based around that. You have a long way to go and once you start adding washing gear, clothes... OS maps etc (you might not need maps in leafy Hampshire or Kent but you sure as hell will when you hit Northern Scotland or the national Parks in Wales) the weight and size builds quick.
I think also you will find you need more than 100quid too.. With the distance you are planning on you will need a few sets of new boots along the way (good boots make the difference between pleasure and utter misery... boy I learnt that the hard way! lol).
I am not criticizing your idea I think its good you have such a sense of adventure but you really need to plan this carefully (read the link someone posted earlier and the pre work that guy did) its not about gathering all the gear and off you go safe as houses, you need to work out if its the right stuff for you first and do you have all the skills you need! reading OS maps is only easy if you know how to do it... at night ... with a torch ... in the pouring rain!
If i were you I'd do a few test runs first ... pack up everything and walk your planned amount of miles, catch your dinner set camp have a wash sleep wake-up and repeat for 3 or 4 days, you will soon get an idea of what work what doesn't, what you need and whats excess weight plus those things you have forgotten (and you will forget something)! lol
There are people on here who know way more than me about kit, skills and prep you may need.. the above its just my experience from my somewhat limited adventures!