How will "modern equipment" allow the Royal Observatory to now avoid some of the effects of light pollution at Greenwich?
It's a little hard to guess what research can be done there -- Today, Greenwich is close to the worst place on Earth to have an observatory: At sea level, in the light dome of one of the largest cities in the world, in a country famous for its clouds and fogs.
The Wikipedia article on the observatory mentions the new telescope and says:

In 2018 the Annie Maunder Astrographic Telescope (AMAT) was installed at the ROG in Greenwich. AMAT is a cluster of four separate instruments, to be used for astronomical research; it had achieved first light by June 2018:

A 14-inch reflector can take high resolution images of the sun, moon and planets.
An instrument dedicated to observing the sun.
An instrument with interchangeable filters to view distant nebulae at different optical wavelengths.
A general-purpose telescope.


At a guess, they hope to do some sort of star position measurements which is one sort of astronomy that is less affected by haze and light pollution (though it needs steady air -- I have no idea what the air steadiness is like there). But even that is still better done with larger instruments in better locations, and by satellites such as Gaia.
It really sounds like a public outreach facility or an undergraduate training site more than a research facility.  It's also worth noting that the pictures show equipment that is at the serious amateur level -- I certainly know amateurs who have better equipment.