You don't "need" to peg a diff. It is mostly done for competition from trials events and winch challenges. And I still don't believe a green lane is really going to be comparable.
pegging simply tries to reduce the amount of movement when the diff is shock loaded such as having wheels way in the air spinning quickly and landing hard. Is this something you find happening a lot in your driving?
Something like this with maybe 35-37" tyres.
I'm not saying pegging is a bad idea, it isn't. But D2 axles are arguably the strongest factory "Rover" axle anyway. And for pegging to work, you need to regularly check and adjust it, on a road car you may find this annoying. A stronger diff centre and HD shafts will for most people provide quite a reliable setup. And while Rover axles have a bad rap, many people run completely stock ones for long periods of time with little to no issues. Doing some pretty extreme stuff.
What sort of money are you planning on spending?
HD rear shafts are £315
https://www.ashcroft-transmissions.co.uk/halfshafts/disco-ii-rear-shafts.html
And ATB centres £335
An ATB front and rear with the rear shafts + fitting will massively enhance the ability of the vehicle and the durability. It's still pricey and will likely set you back just over £1000 if you aren't doing the work yourself, but this is what I'd do if I wanted stronger axles and enhanced capability.
The front HD shaft upgrade is £735 as it includes CV's. This is a lot of money, so I'd only look to doing it, if I found I kept breaking front shafts and CV's.
New HD crown wheel and pinion sounds like a great idea, but will add significant cost. And for non competition use I doubt you'd see the benefit. So again, would probably only look to seriously doing this if I fond myself breaking lots of them or required a ratio change.
At the end of the day, it really would be little issue to drop £4k into beefing up the axles if you really wanted too.
An axle swap may prove a cheaper bet if you are comparing to the ultimate setups. But the question to ask is, what do you need, rather than an ultimate setup?
I really struggle to believe you could perform a complete axle swap for less than £1k though.