By your description you sound like you have combination skin which is severely dehydrated. The dehydration is causing the dullness, the aggravated dryness and most likely the 'aged' look.
So before we get to the basics of a skincare routine, drink plenty of water (especially if you drink a lot of caffeinated drinks, they're only making you more dehydrated). Avoid sugar, alcohol, cigarettes, and everything else you know is shit for you.
The basic 'MN Budget Routine' is usually something along these lines, double cleansing (in the evening, single cleanse in the morning) - acid toning (optional) - serum (optional) - moisturiser - SPF. Full disclosure I'm not UK based (so no access to a lot of the pharmacy brands) and have sensitive skin so I'm no good with recommending budget products from personal use, I'm merely listing the products that are repeatedly recommended here on the S&B boards.
First Cleanse: You want an oil based cleanser (not to be confused with the 'natural' oil cleansing method) to cut through make-up and SPF which you remove with a warm flannel (despite the method being called 'hot' cloth cleansing, hot water is shit for your skin) or a muslin. Use a clean flannel/muslin each day. For mornings (or days when you don't wear make-up and/or SPF) skip this step.
Suggested products: Body Shop Camomile Sumptuous Cleansing Butter or Superfacialist Una Brennan Vitamin C Skin Renew Cleansing Oil.
Second Cleanse: The first cleanse was to remove all make-up, the second is to clean the actual skin and any residue. Gentle is what you want here, a milk or cream cleanser. Ignore instructions of removing with cotton pads etc. Simply apply to dry skin and take off with warm flannel/muslin from above.
Suggested products: Cetaphil Gentle Skin Cleanser, not an S&B but one I've used and fall back on often, Weleda Almond Soothing Natural Cleansing Lotion
Acid toning: The quickest way to kick start your skin again, caution is warranted. Slow and steady is the way to go here, introducing it once or twice a week and building it up to a point that feels comfortable for your skin which can be anything from twice a day to once a week/fortnight. AHA helps break down dead skin cells and encourages cell turnover, revealing more 'youthful' and radiant skin. BHA works deeper down and is good for cleaning out pores and with spots. There are more types of acids and both AHA and BHA are far more complex than described but this is their basic setting. I would only suggest incorporating acids into your routine when you have your basic setup of cleanser - (serum) - moisturiser - SPF in place. If you can't commit to daily SPF and regular top ups during the day in the height of summer do not bother with acid toning, it makes the skin photosensitive, you will only damage and worsen it if not diligent with SPF post acid toning.
Suggested products: AHA - Nip + Fab Glycolic/Glycolic Extreme pads, BHA - Nip+Fab Dragons Blood Fix Pads
Serum: A concentrated and light weight formulation that penetrates skin more effectively than moisturiser. This is where you address your specific skincare needs, hydration, acne, sensitivity, etc. In your case I'd focus on hydration. Focus on anti-ageing when your routine is established and you understand what's working for you and what isn't.
Suggested products: Superdrug Simply Pure Hydrating Serum
Moisturiser: Seals everything in, for whatever reason we're still all stuck on the moisturiser being the most important and life changing product in your skincare routine. It's not. Probably leftover marketing from the anti-ageing overpriced cream era, moisturisers aren't going to do much on their own. Spend your money on serums and get a no frills workhorse.
Suggested products: Go with the one you like already, oft mentioned on the S&B boards are, Eucerin Hyaloron Filler, Aldi Caviar and Aldi CoQ10. Please note that day creams may have an SPF in them, they are by no means sufficient and to avoid clogging your skin unnecessarily do not use an SPF containing day cream at night, you will need to double cleanse it off in the morning. Needless washing results in aggravated skin. The easiest is to have one moisturiser without an SPF in it.
A separate SPF: Beyond its necessity for use with acid toning, it is the most effective anti-ageing product (as well as skin cancer deterrent) as it blocks damaging sun rays from your skin. SPF30 is advised as a minimum year round.
Suggested products: La Roche Posay Anthelios, Biore UV AQUA Rich Watery Essence
Google at your leisure I'm too lazy to link it all up, I'm making a copy of this excessively long piece of text that was meant to be a quick and brief reply, as these type of skincare help questions surface all too often on these boards and I'll try to include any other product suggestions that come up on this thread that I've forgotten about.