It should be noted that this use of have is generally an auxiliary in British English but not in American English. "Have you to leave?" is sometimes acceptable in British English, but American English requires "Do you have to leave?"

@alphabet: "Have you to leave?" would be very strange in British English. (There may be contexts where using this sense of have as an auxiliary is current, but this is not one of them :)

@psmears I find "Have you to leave?" (the stressed form) far from 'very strange' (though "Do you have to leave?" is doubtless more common, even in the UK.) I'm not alone; some even license the unstressed form: << With all respect to jennijenni, I think (s)he is mistaken in qualifying 'Have I to...' as incorrect. Here is an example of that construction in current use on a BBC site ("Ask a Teacher") dealing with examination revision: ...

"_ Practise reading questions carefully. Ask yourself what is the question asking me to do? What does the examiner expect of me? Have I to calculate? Have I to describe? Have I to explain?" _ Wynn Mathieson >> [WordReference_Forum]

@nayfan Because in "I had to leave", "have" is a lexical verb, not an auxiliary, so it doesn't contract.

@EdwinAshworth: Perhaps it is a regional thing (or generational, etc). But even as a stressed form, "Have you to leave" comes across as (at best) affected, to me.

"BillJ 'I'd a feeling that this wasn't the case' sounds acceptable to me. And .100 000 (raw) hits in a Google search for "I'd a feeling that".

@EdwinAshworth: Re "I'd a feeling": see also "I've no idea"/"I'd no idea"

There are numerous examples on the internet of "I'd to [finish an important piece of work / stay in Alicante an extra two nights / ...]" /// and " ... one more place I'd yet to visit" / "two things I'd yet to do", which I doubt anyone would object to. As QED says above, this seems to hinge on how incongruous weak forms sound in strong assertions.

@EdwinAshworth But not normally when it's a catenative verb, as in the OP's example. And the negative ones are best regarded as inflectional forms.

@BillJ There are other analyses; some grammarians regard have to as a semi-modal like ought to and used to rather than have here as a lexical verb.

My sense is that you'd be more likely to contract had in "I had to pick up some things" than in "I had him pick up some things". (But maybe that's just because the first sense seems more usual and commonplace.)

It's just about possible to say I've to leave early tomorrow, so I'm going to bed now. But normally that first verb would be pronounced haff, not have - and to all intents and purposes that (with past tense pronounced hat, not had) is effectively a different verb, which can't normally be contracted.

@StuartF: Hmm. It's often / usually pronounced I HAT to pick up some things, which can't be contracted.

It might just be a Yorkshire thing, but "I'd to leave early to get home in time." wouldn't be unusual, in speech. Perhaps removing the emphasis of 'had' to make the reason more important to the sentence.

@Tetsujin: I suggest it's the opposite, because I'd to leave early to get home in time prevents us from including the emphatic stress on I hat to leave early... Hence that contraction sounds to me more like plain I left early... (or I was to leave early... if departure isn't ongoing/imminent). That's to say, using the contracted form reduces / eliminates the sense of the speaker being obliged to leave early.

@alphabet That is simply not true re the auxiliary in AmE. And by the way, folks, in the utterance, I had to leave. had is not an auxiliary there. It is the main verb.

And yes, agree with Edward and Fumble Fingers.