If you’re talking about Lalla Ward (Romana II), yes, she and Tom Baker were in a relationship at the time. Mary Tamm, the original Romana, I once heard Tom Baker refer to in an interview as “the one with the tits.”
I did mean Lalla Ward, not Mary Tamm.
Must be nice being a space monster with a time travelling portajohn you use to pick up foxy English women! I’ve seen two blondes, a brunette (Sarah Jane), a black girl, and two gingers so far; doesn’t seem to be any clear predilections. Time Lords are serial womanizers, it seems! 
Also, Steven Moffat’s first televised Dr. Who was “Curse of Fatal Death”, with Rowan Atkinson as the Doctor informing Jonathan Pryce’s Master that he was giving up time traveling to be with the companion with whom he fell in love.
Available on youtube and highly recommended.
Not to mention a genius, a Time Agent, a grandfather, and a Centurion. The Doctor prefers to travel with women, but isn’t opposed to having menfolks around.
And don’t tell me he wasn’t interested in Harkness. If you have a pulse, you’re interested in Harkness, and the Doctor has two.
I was amused by how he filched Rose literally out of the arms of her boyfriend Mickey by saying, in a nutshell, “Hey, baby, how would you like a ride in my time machine?”
Of course The Doctor has a sexuality, just because he’s alien and a Time lord he has a sexuality, even a female Silurian fell in love with a human Victorian girl, so I’m guessing despite being a Time Lord he has a sexuality, River Song proves that Time Lords has sexualities and actually I think you wrong, I think The Docor is very comfortable with sexuality and knows sexuality better then anyone to the point where he doesnt care about it, as long as those two people/aliens love each other and are happy. I think The Doctor is straight (although I hate saying that), but I think he’s very open to other genders and races, so open to a point where it looks like he’s pansexual. There’s a couple of examples where he’s shown this as far as the episodes I’ve seen, Christopher Eccelston he gets kissed by Jack and of course The magnificent Rose Tyler is his one true human love, David Tennant was admired by anything that moved, however Matt Smiths the eleventh Doctor is slightly different in that anything that moves still wants to get into bed with him, but because of modern times The Eleventh Doctor isn’t worried about spreading his bets, by actually showing off the people he loves and cares for. I think River Song plays a big part in this. Because The Elenventh Now knows his one true love that matches his mind and capabilities he’s even more sure of himself and this comes out in him kissing Rory and slightly/ overly admiring Amy. I think he admires Amy, I don’t think he loves her sexually, although that can’t be said for her, maybe because he’s destined for River song that it amplifies their love for each other, River can’t always be in The Elenth Docors life, but Amy was more of a continuity and I think that’s what The Doctor likes. I don’t think he loved her sexually though, I think people misconstrued admiration for sexuallity. To Amy The Doctor is a God, to me that’s admiration.
The Doctor had an unusual relationship with Amy. I think she was the first companion that he knew as a child and as an adult.
Giving more of a big brother / sister relationship (his perspective).
Rose was someone the Doctor could have married. He connected with her very strongly.
New Who seems to always create elaborate relationships between the Doctor and companion. It can be frustrating to figure out.
I often preferred the original approach. The companion was just there for the adventure.
The new companion Bill is a return to that, being a lesbian.
I haven’t much Dr Who, but I did see many of the Amy Pond episodes. I found it emotionally jagged to see Amy as a little girl, watch her sass and humour, and then eventually witness her death at the hands of the Weeping Angels. It makes sense that if the Doctor was going to grieve for any of his companions, it was going to be Amy.