5w-40 is a good choice. The only disadvantages with a 5w-40 is that it may be a bit rattly when cold if the engine is worn and the car may use a drop of oil. If it doesn't, then stick with the 5w-40, it gives much better protection than a mineral 20w-50.
Tesco (and all other own brand oils, including Halfords) are very basic. Oil manufacturers bid for the contract, meaning the lowest bidder gets the deal and the oil is made to the lowest spec available (more basic basestock, lower quality additive package). Proper branded oil costs more for a reason, not just a name on the label. Saying that, even a basic synthetic like the Tesco one is a better option than a mineral oil.
Cheers
Tim
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