No, it is not illegal to have different tyre brands or models on your vehicle - as long as the tyres are in good condition and a suitable size and type for your vehicle.
However, it is worthy noting that you should not mix differing tyre makes and tread patterns on the same axle. This can lead to handling issues and reduce the lifespan of the tyres.
It is important to remember that tyres of different sizes should never be used on the same axle, as this can affect the handling of the vehicle and put you at risk of an accident. If you are unsure about the tyres on your vehicle, it is best to speak to a professional for advice.