If your Mk2 has the dim-dip system (headlight dipped beams come on at reduced intensity with headlight switch in the sidelights position), I think there is a change-over relay attached to the fusebox. I suggest unplugging the dim-dip resistor - that leaves you with sidelights when the switch is in the sidelights position, and headlights with the switch in the headlights position - less confusing. Dim-dip was required in the UK from 1987 to 1994 (I think). I don't know why - it seems pointless. Can't think of a case where dimmed dipped headlights are better than dipped headlights.
Sorry I don't have a diagram for the standard relays on the Mk2 Uno.
Since the problem is 'no lights', I think it's likely to be as Louie says - if there is a relay, it's probably not original and has been fitted by someone with good intentions, but poor execution
There obviously is a relay, because you've replaced it, but it must still be worth checking the points Louie gives.
Trace the wiring back from the headlight plug and see what you find. Also, generally by listening to and feeling for relays, you will identify the relay if it is in the standard fusebox. Generally though, you would expect to find a headlight relay somewhere near the headlights if it has been added by someone. A relay fitted near the fusebox could be neat and tidy, and reduce the load on the headlight switch, improving the supply to the standard fuses. But there will still be the potential for poor connections to the standard fuses and the wiring from there to the headlights. So generally, I would fit relays near the headlights.
I think this 'no lights' problem is a good reason to double-up on the relays - one per headlight, one for dipped and another for main - I know that four relays + connectors are expensive when bought new, but such expense is relative when you consider the possiblity of losing all the lights when a single relay dies. Also, one reason for the single relay failing could be the relatively high current drawn by two headlights (about 120W = 10A). Well, the relay is supposed to be rated to 30A, and 10A shouldn't be a problem. But it will be if there are poor connections that get hot.
The relays need a fused, high-current feed. I use the terminal block behind the battery (near the suspension strut turret) - the one with two threaded studs and a snap-fit lid. Use amplifier installation cable and place a large fuseholder nearby. Ideally you would use two fuses - one for left, one for right - as a blown fuse would disable both lights otherwise. But anyway, the important thing is to have a fuse close to the battery, so that if the supply cable chafes on a metal part, you don't have a fire on your hands. From the fuse, the supply cable should be well-protected and routed around the front of the engine bay, to supply the '30' terminal of all relays. Another convenient place to tap into a high-current supply is the starter motor terminal, since that is connected direct to the battery, and is on the front of the Uno Turbo engine.
I use the original headlight wiring to activate each relay coil, then the original headlight plug wires can be attached to the relay normally-open contacts (87). It is worth beefing up the headlight earths a little, too.
After fitting relays in this manner, you'll definitely need to unplug the dim-dip resistor - otherwise you'll get full-strength headlights in the 'sidelights' switch position, which will be confusing because the dip/main beam switch won't work.
If the above ramble makes any sense, I'm sure you're well on the way to making a big improvement to the headlights
If it makes no sense at all, then try doing some Advanced Searches in this forum for 'relay' and 'headlights'.
-Alex
