The paper presents the first results obtained with the Jodrell Bank - IAC two-element 33 GHz interferometer. The instrument was designed to measure the level of the Cosmic Microwave Background (CMB) fluctuations at angular scales of 1 - 2 degrees. The observations analyzed here were taken in a strip of the sky at Dec = +41 deg with an element separation of 16.7 lambda, which gives a maximum sensitivity to ~1.6 deg structures on the sky. The data processing and calibration of the instrument are described. The sensitivity achieved in each of the two channels is 7 micro K per resolution element. A reconstruction of the sky at Dec = +41 deg using a maximum entropy method shows the presence of structure at a high level of significance. A likelihood analysis, assuming a flat CMB spatial power spectrum, gives a best estimate of the level of CMB fluctuations of Delta Tl = 43 (+13,-12) micro K for the range l = 109 +/- 19; the main uncertainty in this result arises from sample variance. We consider that the contamination from the Galaxy is small. These results represent a new determination of the CMB power spectrum on angular scales where previous results show a large scatter; our new results are in agreement with the theoretical predictions of the standard inflationary cold dark matter models.