Hi there,
I've not heard of tablets as an alternative. What can be done though is a natural cycle IVF. That means you take no hormones that would make many follicles grow, but rather, once your one (sometimes two) follicles of the month have reached the right size (seen by ultrasound), they are aspirated (needle into ovary through vagina and flesh), they attempt to fertilise the one (or two) egg cells, and if it works, they re-implant them in your uterus.
This method has the obvious advantage that you don't have to take/inject hormones. However it has the equally obvious disadvantage that you are likely to have to undergo several runs of follicle aspiration. The chances of fertilising a single egg in vitro are not very high. And even if it does (at the first or any subsequent attempt) fertilise, the chances of it implanting in your uterus are also not very high. That's why it is common to transfer two embryos, or even more, in order to increase the chances of success. That said, there is a trend towards single embryo transfer now, with the aim of reducing the 'risk' of multiples.
The hormonal treatment can have potentially serious side effects, such as ovarian hyperstimulation that can in some cases even lead to death. However, I'm not sure that natural cycle IVF is a good solution to this, because each aspiration (and you'd probably need more of them) is also risky - the needle can notch your bladder and cause permanent damage, for instance.
From a cost point of view, I doubt the NHS would pay for natural cycle IVF. If going privately, it might work out about equal - as you'd save on the hormones, but pay for extra treatment (ultrasounds, aspirations).
From what it would 'cost' you, it would probably be longer until you conceive, you'd be in and out of the clinic potentially for months and months. But you would't have to do the injections nor go through the turmoil sometimes caused by the hormones.
HTH.