If the deceased was domiciled within the UK and not a US citizen, generally, no US estate tax will be payable on the US assets due to the double taxation agreement between the US and the UK.
However, there is still the obligation to apply for the clearance certificate by lodging the US estate tax return (usually form 706-NA and supporting forms and documents). The estate may also only benefit from the provisions of the double taxation agreement if this is correctly applied for.