To do a "Good" job of Mains Powered external lights on your site will
not be "easy".
The existing wiring shows that making it look "neat" will not be easy either!
You have been quoted £160 for installation (presumably, without the cost of the lamps themselves).
For this amount, I would expect that you would get the most
basic of installations - and
you would almost certainly need to apply paint etc., to minimize its effect !
You stated
"I did contemplate this (Solar Lights), but not got great experience with the reliability of solar lights, often lasting a few months at best before needing to be replaced, so trying to get a hard wired solution."
Many Solar Lights are made to the cheapest possible "standards" - to sell at the cheapest possible prices.
With many it is not (easily) possible for the user to replace the LED or the Battery and
the Battery is often of the lowest possible "capacity" that the manufacturer can "Ger Away With".
However, some
are made where the Lamp can be replaced by the user and it is usually possible to dismantle
any Solar Lamp and install a higher capacity Cell.
For example, I note that many Solar Lamps are sold with a 3.7V 18650-2200mAh Lithium-Ion batteries.
This is the
"bottom range" of such 18650 batteries but
the same physically sized 18650 batteries are available in "capacities" of up to 9900 mAh - for replacement.
(See
https://www.aliexpress.com/item/1005006892298396.html?spm=a2g0o.productlist.main.13.5f9ffvSAfvSAlk&algo_pvid=d67b0577-d6d0-4462-acec-6b27206ba578&algo_exp_id=d67b0577-d6d0-4462-acec-6b27206ba578-6&pdp_npi=4@dis!AUD!41.11!7.81!!!192.73!36.62!@2103085b17261963362778845e22bb!12000038637212156!sea!AU!3729617017!X&curPageLogUid=32ReONTQ83H3&utparam-url=scene:search|query_from: )
Because of the above, I urge you to reconsider the possibility of installing "quality" Solar Lamps
plus
the possibility of "upgrading" the Battery within them.
(However, I will admit that it may be difficult to obtain information on the battery used before purchasing the product.)
While I do not know anything about them, other than that which is available "on line".
these lamps have replaceable ES "Globes" (which appear to be "Filament LEDs" - although described as Tungsten)
and
appear to have an accessible Battery Compartment.
(They use an AA Battery but
High Capacity AA Batteries are also available.)