I speak American English, and would understand
I hoped that you would consider my application favourably.
to refer to a past hope, for example, spoken by someone whose application had not been considered favorably, or by someone whose application had been considered favorably, if it were spoken jubilantly. In any case, the speaker no longer has the hope, either because the hopes were dashed or otherwise petered out, or because they came to fruition.
The use of the present perfect:
I have hoped that you would consider my application favorably.
strikes my ear as unidiomatic tense-wise. I would say "I have been hoping" if I wanted to convey the idea that my hope has been ongoing for some time now, and that it continues even now.
If I wanted to express the idea that I am in a state of ongoing hope:
I'm hoping that...
or the simple idea that I have a hope:
I hope that...