Noticing a little more travel on brake pedal and handbrake lever and wonder whether some adjustment can be made to reduce this travel on brake pedal

If the hand brake requires more travel, then you must have drum brakes on the rear of the car. The drum brakes an be adjusted as the brake shoes wear. You will have to remove the wheel and the brake drum. There will be an adjusting wheel, often called a star wheel because of its shape. Turning the adjusting wheel in the right direction will expand the brake shoes, thereby eliminating some of the travel required before they contact the brake drum. You will have to use a screwdriver with a flat blade to turn the wheel. Turn the wheel a little, then test fit the brake drum. Keep doing this until the brake drum goes on with a slight resistance. Replace the wheel, and proceed to the other side of the vehicle and repeat the process on the other rear brake. This should give you a better feel in the brake pedal and the parking brake.

Your rear brakes are worn or the self adjusters are rusted, assuming you have drum rear brakes & not disc pads in the rear.
Try backing up several times with very hard stops to activate the self adjusters. If you don't back up much, the self adjusters can not work. Parking brake will be adjusted at the same time.

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