The Travel.SE recurring suggestion is good advice. We would advise you to follow it, and for exactly the reason you state.

Many Travel.SE questions have addressed this issue. Use the "Search on Travel" box at the top of the page, and search for "Find UK Solicitor." One useful Q&A is this one.

Did your wife's UK visa application mention that you would be staying in the home country (I presume Kenya) while she sits the PLAB2 exam? Your presence at home during her UK visit would provide home country ties for her, and could have been important to UKVI's approval of her visa application. You are now saying that this particular fact of her application may not turn out to be true; this might imperil her already-granted visa. Before your file your own application, consider consulting with a UK solicitor who deals with UK visa issues.

Money on deposit isn't much of a tie to your home country, because money is portable. That you have a job has some weight and it's right to have your employer's express agreement (as you do) to your vacation. OTOH, your wife's being in the UK is a strong negative for your visa application: she is presumably your closest relative, and her presence in the UK will be seen as a situation that'd make your overstaying in the UK more likely than if she were in the home country while you traveled.

The UK Home Office page cited by @JohnDoe in his comment to the original question contains language that provides an exemption from the visa requirement for those who hold a valid D-visa, such as the OP. Do you think this UK page is inapplicable to the OP?

To continute @MichaelSeifert's comment: Gatwick airport doesn't have a secure transit facility. To fly into Gatwick, every passenger must pass UK Immigration and be admitted into the UK. A passenger who is not eligible for admission into the UK will be denied boarding, even if holding a paid-for ticket on that flight.

In addition to the airport info requested in the above comment, knowing the flight numbers and airlines might also be useful in responding to your question.

Does the train leave from Copenhagen central station? What time does the train depart for Malmö?