As for the cheap dual rail PSUs, any pointers for what to look for? The 19V 65W laptop bricks are readily available and cheap here, but haven't found anything dual rail that's available and not considerably more expensive.
Hmm, after a quick look, neither have I.

But will investigate further and list any approaches that may be of interest.
[1]
SINGLE MAINS SUPPLY WITH +- 18V RAIL OUTPUTSWith this approach, the mains PSU provides stabilized +-18V supply rails directly from the mains.
This is the board that I originally had in mind, but it is only generates +-15V at 500mA:
https://www.ebay.co.uk/itm/HIFI-Single-voltage-to-positive-negative-Regulator-powerFinished-board-Low-noise/253615314877?_trkparms=aid%3D222007%26algo%3DSIM.MBE%26ao%3D1%26asc%3D20170920101022%26meid%3D8b93c439f71147b7ad5c5d353e5d1c86%26pid%3D100010%26rk%3D3%26rkt%3D3%26sd%3D262381275345%26itm%3D253615314877&_trksid=p2047675.c100010.m2109After a good search, I could not find any low-cost +-18v, at 1A or greater, SMPSUs, so it looks like this avenue is a dead end as far as your application is concerned.
[2]
TWIN MAINS SUPPLIES TO PROVIDE +- 18V RAILSAs capt bullshot says in reply #8, two isolating mains supplies can be connected in series to generate the +-18V stabilized supply lines. This is a really neat approach and provides a good performance.
Most, if not all laptop PSUs are isolating and seem to have a fairly standard topology. I suspect that many of the laptop PSU guts are made by the same company.
If you wanted to make a tidy single PSU, you can remove the plastic cases by running a hot knife down the seams to expose the guts, which are quite compact. Then just put the two PCBs in a nice little metal case for good screening (ensure adequate heat-sinking/ventilation). With a bit of work, you could make a really professional job of it.

This laptop PSU is low cost and has an adjustable output voltage:
https://www.banggood.com/96W-Multi-Function-Universal-Notebook-Laptop-AC-DC-Power-Adapter-Charger-p-981672.html?gmcCountry=GB¤cy=GBP&createTmp=1&utm_source=googleshopping&utm_medium=cpc_bgs&utm_content=frank&utm_campaign=pla-uk-elc2-brand-pc&gclid=Cj0KCQiAmuHhBRD0ARIsAFWyPwgEjaMVK15etZSdrOWzIJcf2mH17DD_pm715GJglHzqy1JiPcMQ4i8aArdxEALw_wcB&cur_warehouse=CNBut you are not limited to laptop SMPSUs. There are other suitable PSUs, including, board-level, wall-wart, chassis, and cased.
Here is an example from the many 18V SMPSUs available:
Output current: 4A maximum
Mains supply: international
Size: 110mmx79mmx36mm
Make: Velika
Cost: 91.84 NOK ($10.84US) delivered (free) to Norway
https://www.aliexpress.com/item/Small-Volume-Single-Output-18V-4A-72W-Switching-power-supply-Source-Transformer-100-240V-AC-DC18V/32837291241.html?ws_ab_test=searchweb0_0,searchweb201602_5_10065_10068_10130_10547_319_317_10548_10696_10192_10190_453_10084_454_10083_10618_431_10307_10820_10301_10821_10303_537_536_10059_10884_10887_100031_321_322_10103,searchweb201603_51,ppcSwitch_0&algo_expid=d54973ac-b655-42ea-9574-477d33b908af-20&algo_pvid=d54973ac-b655-42ea-9574-477d33b908af&transAbTest=ae803_5[3}
TWIN 24V OP MAINS SMPSUs AND +-18V LINEAR REGULATORSHere twin mains SMPSU provides +-24V which is regulated down to +-18V by a pair of complementary three-terminal linear regulators (LM317/LM337 etc). This arrangement can be made suitable for-high end audio pre amplification, but filtering out the switching hash, from the two SMPS to negligible levels, would take some doing. And the 0V line would be problematic.
Mains PSU with 24V OutputOnce again, there is any number of suitable low-cost 24V mains SMPS. Here is just one example:
https://www.banggood.com/4A-To-6A-24V-Switching-Power-Supply-Board-AC-DC-Power-Module-p-969204.html?rmmds=search&cur_warehouse=CN[4]
MAINS SUPPLY AND +-18V GENERATORWith this approach, a mains to DC SMPSU powers a board that generates +-18V supply rails.
Mains 4V to12V SMPSUWith the +- supply line generator described below, a mains to 4V to 12V, 52W min PSU would be required. There is an endless choice of suitable PSUs, especially with 12V outputs, which would be the best output voltage. An example would be the 12V, 5A SMPS from here:
https://www.ebay.co.uk/itm/DC-12V-24V-5V-10A-12-5A-15A-20A-30A-Universal-Regulated-Switching-Power-Supply-/181881169501+- Supply Line GeneratorInput supply: 4V to 12V
Output supplies: +- 8V to +-18V adjustable @ 1A5
https://www.ebay.com/itm/HIFI-Regulated-Power-Supply-Single-Voltage-To-Positive-And-Negative-Power-Output/253689999076?_trkparms=aid%3D222007%26algo%3DSIM.MBE%26ao%3D1%26asc%3D20131231084308%26meid%3D50b108bfc6f043fe879ece914a932086%26pid%3D100010%26rk%3D2%26rkt%3D5%26sd%3D272417883151%26itm%3D253689999076&_trksid=p2047675.c100010.m2109[5]
ROLL YOUR OWN +- 18V OUTPUT SMPSThis would be good fun and not too difficult to do, but more of project in its own right rather than a means to an end.
[6]
MAINS TRANSFORMER/ DIODE/ RESERVOIR CAPACITOR WITH OR WITHOUT +- 18V REGULATORSThe title is self explanatory.
This is the Rolls Royce approach that is not difficult to design and build: with the appropriate components and layout, suitable for high-end audio pre amp stages.
CONCLUSIONWhich is the best approach? To me one wins hands down.
