Is the patio space marked all of the garden, or is there more? Under permitted development one of the rulings is that 'future buildings should not cover more than half of the original land.', thus you may not be able to convert the garage and have the extension under permitted development.

If there is more garden. then of course it's still possible.

Bearing in mind, you need change of use for the garage, so that therefore becomes part of the house and in doing so uses up some of the footprint available. ( also it depends on when things were built ) The rule comes in to play because you are adding another extension and connecting the two. So you are still in effect ( in my opinion ) overstepping the permitted development rule.

If you were JUST converting the garage it wouldn't be a problem.

If you were JUST constructing an extension, it wouldn't be a problem.

Do you know why the plans were rejected? Is it worth pursuing?

You would need to clarify from the planning department, when the garage was built? If it is included in the footprint of the original building, and, with regards the extension :- Make sure it's not covering more than half the ground that the original building was built on.

Here's a couple of links to the relevant pages on the planning portal:-

Permitted development

Garage conversions

Lofts are now considered a separate entity, so don't come under the same rule. There are rules for lofts and you can only increase the size by a certain percentage depening on whether Terraced, Semi or detached - that's also on the Planning Portal, it's a useful tool.

With regards the extension, don't forget that permitted is restricted usually by the 3m rule and as you want to add in the garage, it may use up most of that by itself. You may be able to get around it by using the 'conservatory rule'. Depending on the amount of glass used in the 3m extension, you may be able to claim it as a conservatory instead of an extension, thus you would be able to convert the garage and have a conservatory.