The Succession to the Crown Act 2013 did not grant any succession rights to the British Crown to descendants who were rendered illegitimate in English law by the Royal Marriages Act 1772. They remain excluded from the throne.
By virtue of Subsection (5) of the 2013 act, which is quoted in Benjamin's post above, certain (not all) marriages which were void under the Royal Marriages Act have been retroactively made valid, imparting legitimacy to their formerly illegitimate descendants.
However, Subsection (6) carves out an exception: The formerly-void marriages continue to be treated as void
for purposes relating to the succession to the Crown. In other words, where the British throne is concerned, the descendants of these marriages continue to be treated as if they were illegitimate (and illegitimate descendants are barred from inheriting the British throne).
From the Succession to the Crown Act:
3 Consent of Sovereign required to certain Royal Marriages
[...]
(4) The Royal Marriages Act 1772 (which provides that, subject to certain exceptions, a descendant of King George II may marry only with the consent of the Sovereign) is repealed.
(5) A void marriage under that Act is to be treated as never having been void if—
(a) neither party to the marriage was one of the 6 persons next in the line of succession to the Crown at the time of the marriage,
(b) no consent was sought under section 1 of that Act, or notice given under section 2 of that Act, in respect of the marriage,
(c) in all the circumstances it was reasonable for the person concerned not to have been aware at the time of the marriage that the Act applied to it, and
(d) no person acted, before the coming into force of this section, on the basis that the marriage was void.
(6) Subsection (5) applies for all purposes except those relating to the succession to the Crown.
https://www.legislation.gov.uk/ukpga/2013/20/section/3/enacted
Therefore, even
if British authorities would deem it "reasonable for [Victoria Melita] not to have been aware at the time of the marriage [to Kirill] that the [Royal Marriages] Act applied to it", her descendants by Kirill are continually excluded from the British throne (except, of course, for those who happened to inherit succession rights from a separate ancestor outside of Victoria Melita's lineage, as Gawin mentioned upthread).
As for whether Victoria Melita was "aware" that the Royal Marriages Act applied to her second marriage to Kirill, adding to Gawin and Prinsara's points, Victoria Melita was aware enough of the Act to request (and receive) the British sovereign's consent to her first marriage, even though she was already a member of a foreign royal family (the ducal house of Saxe-Coburg and Gotha) at the time of her first marriage and was marrying into another foreign royal family (the grand-ducal house of Hesse).