Not sure airlines themselves are in a position to give assurances/guarantees, if we ask we get referred to UK Government sources such as the one here:
https://www.gov.uk/guidance/air-serv...l#introduction
Introduction
The EU’s Regulation 2019/502 on common rules ensuring basic air connectivity (‘the EU Regulation’) entered into force in March 2019. This Regulation provides the basis for EU countries to give UK airlines permission to operate if the UK leaves the EU without a deal. Subject to some minor modifications, it also applies to Norway and Iceland through its incorporation into the EEA Agreement.
The EU’s Regulation was originally intended to apply until the end of March 2020, but a proposal to extend this to October 2020 was announced by the European Commission on 4 September 2019. The rights the Regulation provide to UK airlines are conditional on the UK granting equivalent rights to airlines from EU countries.
In March 2019, the UK published a policy statement setting out the UK position on rights for airlines from EU countries to operate for the duration of the EU Regulation. This statement was also intended to apply until end of March 2020. In order to provide more certainty for consumers and industry, the UK also proposes to extend the period for which these contingency measures apply to cover the 2020 IATA summer season (which lasts until 24 October 2020), for air services between the UK and the EU. This proposal remains subject to reciprocity by the EU.
My guess can't see any obvious reason why LHR-DXB nonstop should be a problem...anything into Europe
might IMHO get a bit more complex ..looks like flights will operate but I guess there's an off chance it might start to get messy if flights/pax/crew start to get tangled up with customs/immigration associated delays and that in turn starts to have knock on effects on schedules.